This is a mirror of the main homepage of G.L. Litvinov at the Independent University of Moscow

Grigory L. Litvinov

Institutional Addresses:
                          INDEPENDENT UNIVERSITY OF MOSCOW (IMU)
                          and the RUSSIAN-FRENCH LABORATORY "J.-V. PONCELET"
                          Bol'shoi Vlasievskii per., 11
                          Moscow 119002, Russia
                          Phone: (7-495) 241 4086
                          E-mail: islc@dol.ru
                                  glitvinov@mail.ru


Home Address:
                          Nagornaya, 27 - 4 - 72
                          Moscow 117186, Russia
                          Phone: (7-495) 127 3804

Personal Data:

Birthday:                 May 16, 1944

Birthplace:               Russia, Moscow

Citizenship:              Russia


Education and degrees:

1966-1969                 Moscow State University,
                          Ph.D. in Mathematics.

1961-1966                 Moscow State University, B.S. and
                          M.S. in Mathematics


                EXPERIENCE IN HIGH EDUCATION

 INSTITUTION                  RANK                DATES

 Independent University       Research fellow     2002 -
 of Moscow                    and lecturer        Present

 International University     Visiting professor  Sep. 2005 -
 Bremen                       of mathematics      June 2006

 ICSL Mathematical            Professor of        1992-2002
 College                      mathematics

 Moscow State University      Part-time Lecturer  1998 and
                                                  1971-1972

 Moscow State Correspondence  Part-time Senior    1973-1974
 Pedagogical Institute        Lecturer

 Engineering Academy          Assistant           1969-1973
 Moscow                       Professor


             RESEARCH AND INDUSTRIAL EXPERIENCE

  INSTITUTION                 RANK                DATES

 Russian-French Laboratory    Researcher          2006-
 "J.-V. Poncelet"                                 Present

 Independent University       Research fellow     2002-
 of Moscow                                        Present

 Institute for New            Deputy Director     1990-2002
 Technologies,                of the Center
 Center for Optimization
 and Mathematical Modeling

 Soviet-Bulgarian             Chief Expert        1988-1990
 Computer Joint Venture
 "Lingvotehnika"

 All-Union Patent Library     Head of Software    1987-1988
                              Department

 All-Union Research Institute Head of Software    1977-1987
 of Documents and Archives    Department

 All-Union State              Project Manager     1973-1977
 Institute of Statistics
 Technology


        MEMBERSHIP IN HONORARY OR PROFESSIONAL SOCIETIES

     Moscow Mathematical Society

     American Mathematical Society


             SERVICE TO MATHEMATICAL COMMUNITY

     Member of the Editorial Council of the "Russian Journal
     of  Mathematical  Physics".  


                    AWARDS  AND  HONORS

     Soros & Russian Acad. Nat. Sci. Award and Diploma for 1993

     2000 Science/Interperiodica Award and Diploma for the best
   publication in 1999 from Russian Acad. Sci. and Pleiades Publ.


                    INVITED LECTURER at


                                                    Dates

Independent University of Moscow                   September 2006
                                                   May 2007
Lecture course title: "The Maslov
dequantization and tropical mathematics


International University Bremen                    September 2005
                                                   - June 2006
    Lecture courses:

    - "Numerical analysis",
    - "Analysys-2 and ODE",
    - "Linear algebra, probability and
       statistics",
    - "Integration and manifolds".


Voronezh Winter mathematical School - 2004         January -
                                                   February
    Lecture course title: "The Maslov              2004
dequantization and idempotent (tropical)           
mathematics"

The Fields Institute for Research in               June 2002
Mathematical Sciences (Toronto, Canada)

    Lecture course title: "Smooth and
    Nonsmooth Interval Analysis"

Voronezh Winter Mathematical School-2000           January -
(Voronezh, Russia)                                 February
                                                   2000
   Lecture course title: "Idempotent               
   Mathematics and Applications"

Moscow State University                            February - 
                                                   - May 
   Lecture course title: "Idempotent               1999
   Mathematics"

Istituto per le Applicazioni del Calcolo           November,
"Mauro Picone" (Rome, Italy)                       December
                                                   1995
   Lecture course title: "Idempotent Analysis
   and computer calculations"

Oslo University (Oslo, Norway)                     March, April
                                                   1995
   Lecture course title: "The theory of
   non-unitary representations of Lie
   groups and the orbit method"

Belorussian State University (Minsk, Belorussia)   May 1993

   Lecture course title: "Approximations
   and Errors"

All-Union Winter Mathematical School
(Voronezh, Russia).                                1990

   Lecture course title:  "Rational
   Approximations"

Moscow State University                            1971-1972

   Lecture course title:  "Representations
   of Groups and Topological Group Algebras"


             COLLOQUIUM AND CONFERENCE LECTURES

                                                        Dates

Workshop on Convex Analysis (Moscow State University,  Feb 2 - Feb 5
Moscow, Russia; invited speaker)                       2007

International Conference "OPERATOR ALGEBRAS AND        Jan 29 - Feb 3
TOPOLOGY" (Moscow State University, Moscow, Russia;    2007
invited speaker)

International Conference "INTERVAL-06" (St. Petersburg  July 2006
State University, Peterhof, Russia; invited speaker)

International University Bremen (Bremen, Germany)      Oct. 2005

International Conference "Methods of Logic in          July 2005
Mathematics" (Euler International Mathematical
Institute, St. Petersburg, Russia; invited speaker)

International Conference " Harmonic Analysis on        April 25-29
Homogeneous Spaces, Representations of Lie Groups      2005
and Quantization" (Tambov State University, Tambov,
Russia; invited speaker)

International Conference "Topology, Analysis and       Feb. 14-18
Applications in Mathematical Physics" (Moscow State    2005
University, Moscow, Russia; invited speaker)

Max Planck Institute for Mathematics
(Bonn, Germany)                                        July 2004

Bonn University Institute for Applied Mathematics
(Bonn, Germany)                                        July 2004

International Conference "Representation theory,       June 8-13
Dynamical Systems, and Asimptotic Combinatorics"       2004
(Euler International Mathematical Institute,
St. Petersburg, Russia; invited speaker)

Charles University in Prague (Czech Republic)          April 2004

International Conference "Geometry and Combinatorics
in Physics" (Independent University of Moscow,         March 2-7
Moscow, Russia; invited speaker)                       2004

Moscow State University (Math. Dept.,Moscow)           March 1
                                                       2004

Inernational 25th Linz Seminar on Fuzzy Set            Feb. 3-7
Theory "Mathematics of Fuzzy Systems" (Linz            2004
University, Linz, Austria; invited main speaker)

International Conference "Kantorovich Memorial.        Jan. 8-13
Mathematics and economics: Old problems and            2004
new approaches" (Euler International Mathematical
Institute, St. Petersburg, Russia; invited speaker)

International Workshop "Amoebas and tropical           Oct. 22-27
geometry" (American Institute of Mathematics,          2003
Palo Alto, California, USA, invited speaker)

University of California in San Diego, USA             Oct. 2003
                                                       
International Workshop on Max-algebra (IWMA;           June 30 -
University of Birmingham, Birmingham, UK;              July 3, 2003
invited speaker)

Steklov Mathematical Institute of the Russian          March 29
Academy of Sciences (S.- Petersburg division)          2003

Institute for Theoretical and Experimental             March 17
Physics (ITEP,  Moscow)                                2003

International Workshop "Idempotent Mathematics         Feb. 3-10
and Mathematical Physics" (Erwin Schroedinger          2003
International Institute for Mathematical Physics,
Vienna, Austria; organizer and invited speaker)

The 2002 Twente Conference on Lie Groups               Dec. 16-18
(Twente, the Netherlands; invited speaker)             2002

International Workshop "Representation Theory          Dec. 9-13
of Lie groups, Harmonic Analysis on Homogeneous        2002
Spaces and Quantization" (Lorentz Center,
Leiden, the Netherlands)

Lund University (Lund, Sweden)                         November-
                                                       December 2002

Independent University of Moscow  (Globus              Oct. 10, 2002
Semin., Moscow, Russia)

Centre Universitaire de Luxembourg (Luxembourg)        September-
                                                       October 2002

Universite de Metz (Metz, France)                      September-
                                                       October 2002
                                                       and Feb 3, 1995

International Conference on Harmonic Analysis          Sep. 9-12
(Luxembourg-Metz; invited speaker)                     2002

University of Toronto (Toronto, Canada)                June 2002
                                                       January and
                                                       February 1996

University of Salerno (Salerno, Italy)                 Dec. 2001

University of Tunis (Tunis, Tunisia)                   Oct. 2001
                                                       
Journees de Physique-Mathematique "Analyse             Oct. 10-11
Harmonique et Quantification" (Faculte des             2001
Sciences de Sfax, Sfax, Tunisia; invited
speaker)

International Workshop "Topology, Analysis,            Aug. 29-31
and Related Topics" (Moscow State University,          2001
Moscow, Russia; invited speaker)

European summer school "Asymptotic                     July 16-18
combinatorics with applications to                     2001
mathematical physics" (NATO Advanced Study
Institute and the Euler International
Mathematical Institute, St. Petersburg; 
invited speaker)

St. Petersburg Mathematical Society Meeting            May 22
 Title: "Idempotent Mathematics                        2001
 and Mathematical Physics"

Istituto per le Applicazioni del Calcolo               May 2001
"Mauro Picone" (Rome, Italy)

Univ. of Rome "La Sapienza" (Rome, Italy)              May 2001

European School in Group  Theory                       Aug. 14-26
(SDU-Odense University, Denmark; invited speaker)         2000

11th IFAC International Workshop "Control              July 3-6
Applications of Optimization" (St. Petersburg,         2000
Russia; invited speaker)

6th International IMACS Conference on                  June 25-28
Applications of Computer Algebra (St.                  2000
Petersburg, Russia; invited speaker)

Erwin Schroedinger International Institute             Apr. 2000
for Mathematical Physics (Vienna, Austria)             October and
                                                       November 1998
                                                       May 1996

International Conference on Rational                   June 6-11,1999
Approximation (Antwerp, Belgium;
invited speaker)

International Meeting "Braude College Days             May 1999
of Differential Equations and Applied Analysis
(Karmiel, Israel; invited speaker)

Technion (Haifa, Israel)                               May 16, 1999

Univ. of Haifa (Haifa, Israel)                         May 11, 1999

Univ. Bar-Ilan (Tel-Aviv, Israel)                      May 9, 1999

Mathematical Institute, Leiden University              April 1999
(Leiden, The Netherlands)                              April 1997
                                                       May 1994

Univ. de Valenciennes (Valenciennes, France)           February 1999
                                                       November 1997

Univ. de Lille (Lille, France)                         February 1999
                                                       November 1997

International Colloquium "Idempotent Analysis"         January 1999
(Caen, France; invited speaker)

Sophus Lie Workshop (Kazan, Russia;                    Sept. 7-17,
invited speaker)                                       1998

International Conference Dedicated to the              Aug. 31-
90th Anniversary of L.S.Pontryagin                     Sept. 6, 1998
(Moscow, Russia; invited speaker)

International Conference "Geometric                    August 1998
Analysis'98" (Kiel, Germany; invited speaker)

Lobachevsky Meeting, Kazan University                  December 1997
(Kazan, Russia; invited speaker)

Univ. Paul Sabatier (Toulouse, France)                 November 1997

S.G.Krein Conference on Functional Analysis            October 1997
and Mathematical Physics (Voronezh, Russia;
invited speaker)

International Workshop on Idempotent Analysis          April 4, 1997
(Nottingham, England; invited speaker)

International Conference "Interval-96"                 October 1996
(Wuerzburg, Germany; invited speaker)

International Workshop "Harmonic Analysis              August 1996
on Homogeneous Spaces" (Tambov, Russia;
invited speaker)

Moscow State University (Moscow, Russia;               April 1996
Faculty Seminar)

University of Miami (Coral Gables, USA)                March 22, 1996

Pennsylvania State University (University              March 19, 1996 and
Park, USA)                                             Nov. 13, 1990

University of California (Riverside, USA)              March 12, 1996

Northeastern University (Boston, USA)                  March 4 and 8, 1996

University of Michigan (Ann Arbor, USA)                Feb. 29, 1996 and
                                                       Oct. 19, 1990

University of Missouri-St.Louis (St.Louis, USA)        Feb. 26, 1996

International Conference on Harmonic Analysis          December 1995
(Delhi, India; invited speaker,
Sci. Committee member)

Fifth Workshop on Representation Theory of             August 1995
Lie Groups and its Applications
(Cordoba, Argentina; invited speaker)

Univ. Pierre et Marie Curie (Paris, France)            Feb. 10, 1995
                                                       

Ecole Polytechnique (Palaiseau, France)                Jan. 31, 1995
                                                       

LAAS - CNRS seminar, Toulouse, France                  Jan. 26,27
                                                       1995

Workshop on Models of Parallel Computations            December 1994
I.A.C.- C.N.R., Rome, Italy (Invited speaker)

Hewlett-Packard's Basic Research Institute in          October 1994
Mathematical Sciences (BRIMS) (Bristol, England)
(Idempotency workshop, invited speaker)

The University of York                                 October 1994

The University of Nottingham                           October 1994

Classical and Quantum Geometry of Homogeneous          August 1994
Spaces, International Conference, Moscow
(Invited speaker)

Math. Inst., Oslo University (Oslo, Norway)            June 1994 and
                                                       May 1993

American Mathematical Soc. Summer Meeting              August 1993
(Seattle, USA, invited speaker)

International Lie-Lobachevsky                          Oct. 26-30,
Colloquium (Tartu, Estonia, invited                    1992
speaker)

International Conf.on Interval and                     Sept. 22-26,
Stochastic Methods in Sci.and Eng.                     1992
(Interval-92), Moscow

University of Edinburgh, Scotland                      May 21, 1992
(Analysis Seminar)

King's College (University of London)                  May 14, 1992
(Modern Analysis Seminar)

School of Mathematical Sciences                        May 13, 1992
University of North London (Special Seminar)

Purdue University                                      Oct. 17, 1990
School of Science at Indianapolis
Department of Math.Sci at IUPUI (Colloquium)

Massachusetts Institute of Technology                  Oct. 13, 1990
(D.Vogan's Seminar on Lie Groups)

Moscow Mathematical Society Meeting

   Title: "Rational Approximations and Error           March 5, 1991
   Auto-correction"

   Title: "Representations, Ideals, Characters"        1978

Leningrad State University                             Feb. 27, 1991

Leningrad Mathematical Society Meeting                 Feb. 26, 1991

All-Union Winter Mathematical School (Voronezh)        1976-1989, 2000, 2004

All-Union School on Operator Theory                    1977, 1979, 1989

     AND SO ON


                    RESEARCH INTERESTS:

     Representation Theory and Lie groups

     Functional Analysis

     Hypergroups

     Rational Approximations. Theory and Applications

     Computer Technology  (Algorithms and  special  hardware and software)

     Idempotent Mathematics

     Mathematical Modeling and Optimization

     Numerical Analysis and Interval Analysis

        PUBLICATIONS OF G.L. LITVINOV:

     More than 185 publications and books in Russian and in English, a list
     of selected publications is included.  A full list of publications
     is available here.


               List of selected publications

             SELECTED PUBLICATIONS IN RUSSIAN:

     1. Ordinary  Differential Equations - Lecture Notes for
Students of the Engineering Academy. - In: Textbook on  Calculus. -
Moscow, Eng. Acad. Publ., part II, 1974, p. 173-207; part III,
1975, p. 116-188.

     2.  Editor   and  one   of  the  authors  of  the  book
"Mathematical Algorithms and Programs for Small Computers" -
"Finances and Statistics" Publ., Moscow, 1981, 112 pp.

     3. Approximation  properties of  locally convex  spaces
and the  trace problem.  - In:  Theor.Funktsii, Funktsional.
Anal. i Prilozhen, vol.39, 1983, p.73-87.

     4. Approximate  Construction of Rational Approximations
and an Effect of Error Auto-correction. - In: Mathematics and
Modeling -  USSR Academy of Sciences Publ., Puschino, 1990,
p.99-141.


             SELECTED PUBLICATIONS IN ENGLISH:

     5. On Completely Irreducible Representations of Complex
and Real Nilpotent Lie Groups. - Functional Anal.Appl.Vol.3,
# 4, 1970, p.332-334.

     6. Group  Algebras of  Analytic Functionals  and  their
Representations. -  Soviet Math.Dokl.,  Vol.11, #  1,  1970,
p.191-193.

     7. The  Laplace Transform  on Lie  Groups. - Functional
Anal.Appl. Vol.6, # 2, 1972, p. 76, 77.

     8. Characters  and  Simple  Representations.  -  Soviet
Math. Dokl., Vol.15, # 1, 1974, p. 179-183.

     9. On Traces of Operators and Characters of Irreducible
Representations in  Locally Convex  Spaces. -  Soviet  Math.
Dokl., Vol.15, # 1, 1974, p. 308-312.

     10. (with  G.B.Shpiz) Primary Decompositions of Finite-
Dimensional Representations  of Lie Algebras and Lie Groups.
- Functional Anal.Appl., Vol.12, # 2, 1978, p. 149-151.

     11.  Traces  of  Linear  Operators  in  Locally  Convex
Spaces. - Functional Anal.Appl. Vol.13, # 1, 1979, p. 60-62.

     12. (with  L.I.Vainerman). The  Plansherel Formula  and
the Inversion Formula for Generalized Translation Operators.
- Soviet Math.Dokl., Vol. 23, # 1, 1981, p. 333-337.

     13. (with  V.I.Lomonosov). Density  Theorems in Locally
Convex Spaces  and  Irreducible  Representations.  -  Soviet
Math. Dokl., Vol. 23, # 2, 1981, p.372-375.

     14. (with  A.P.Kryukov and A.Ya.Rodionov). Construction
of  Rational  Approximations  by  Means  of  REDUCE.  -  In:
Proceedings of  the 1986 Symposium on Symbolic and Algebraic
Computation.  Symsac'86   (July  21-23,     1986,  Waterloo,
Ontario), Univ.of Waterloo, 1986, p. 31-33.

     15. Hypergroups  and Hypergroup  Algebras. - Journal of
Soviet Math., Vol. 38, 1987, p. 1734-1761.

     16. Representations  of Groups in Locally Convex Spaces
and  Topological   Group  Algebras.  -  Selecta  Mathematica
Sovietica, Vol. 7, # 2, 1988, p. 101-182.

     17. On  Conditions  under  which  a  Representation  is
Determined by  its Character,  up to  Equivalence. - Selecta
Mathematica Sovietica, Vol. 8, # 1, 1989, p. 73-97.

     18. On the Traces of Linear Operators in Locally Convex
Spaces. -  Selecta Mathematica  Sovietica, Vol.8, # 3, 1989,
p. 203-212.

     19. (with  V.I.Lomonosov). Density  Theorems in Locally
Convex  Spaces   and  Applications.  -  Selecta  Mathematica
Sovietica, Vol.8, # 4, 1989, p. 323-339.

     20.  (with   B.M.Levitan).   Generalized   Displacement
Operators. -  Encyclopaedia of  Mathematics, Vol.4. - Kluwer
Academic Publ., 1989, p. 224-228.

     21. Nuclear  Operator. -  Encyclopaedia of Mathematics,
Vol.6. - Kluwer Academic Publ., 1990, p. 487-490.

     22. Nuclear  Space.  -  Encyclopaedia  of  Mathematics,
Vol.6. - Kluwer Academic Publ., 1990, p. 490-493.

     23.  General  Concepts  of  Quantum  Mechanics.  -  In:
F.A.Berezin  a.o.,   The  Schroedinger   Equation  -  Kluwer
Academic  Publ.,  Dordrecht/Boston/London.  1991,  p. 1-49 +
p. 386-415 + p. 462-465.

     24.  Generalized   Translation  Operators   and   their
Representations. -  Selecta Mathematica Sovietica, vol.10, #
4, 1991, p. 307-337.

     25. Double  Topological Algebras  and Topological  Hopf
Algebras. -  Selecta Mathematica  Sovietica,  vol.10,  #  4,
1991, p. 339-343.

     26. Approximation  Properties of  Locally Convex Spaces
and the  Problem of  Uniqueness of  the Trace  of  a  Linear
Operator. -  Selecta Mathematica  Sovietica,  vol.11,  #  1,
1992, p. 25-40.

     27. (with  G.B.Shpiz). Primary Decompositions of Finite
Dimensional Representations  of Lie Algebras and Lie Groups.
- Selecta Mathematica Sovietica, vol.11, # 1, 1992, p. 41-54.

     28. Error  Auto-Correction in  Rational Approximation -
Proc. Intern.  Conf. on  Interval and  Stochastic Methods in
Science and  Engineering (Interval-92), Moscow, 1992, vol.2,
p.59-63; Interval Computations, 1992, # 4(6), p. 14-18.

     29. Approximate Construction of Rational Approximations
and  an  Effect  of  Error  Auto-correction.  Applications  -
Russian Journal of Mathematical Physics, vol. 1,  # 3, 1994,
p. 313-352. See also E-print arXiv:math.NA/0101042 

     30. (with V.P. Maslov).  The Correspondence  Principle  for
Idempotent  Calculus  and  Some Computer Applications; Preprint
IHES, Bures-sur-Yvette, 1995; the same in: Idempotency/
J. Gunawardena (Editor), Cambridge University Press, Cambridge,
1998 (ISBN 0-521-55344-X), p. 420-443. see also E-print arXiv:
math.GM/0101021

     31. (with V.P. Maslov). Idempotent Mathematics: Correspondence
principle and applications// Russian Mathematical Surveys, v.51,
# 6, 1996, p. 1210-1211.

     32. (with V.N. Tulovsky). Generalized Fourier Transform, 
Maslov's Canonical Operator and Hypergroups. - International 
Sophus Lie Center, Moscow, 1997.

     33. Five articles on Idempotent Mathematics for the
Encyclopaedia of Mathematics, - Kluwer Acad.Publ., Suppl. vol. 1,
1997, p. 312-317.

     34. (with B. Komrakov, I.Krasil'shchik, and A.Sossinsky, Editors).
Lie Groups and Lie Algebras, their Representations, Generalizations,
and Applications. - Kluwer Acad.Publ., Dordrecht et al., 1998.

     35. (with K. A. Ross et al., Editors). Harmonic Analysis and
Hypergroups ("Trends in Mathematics" series). - Birkhauser, 1998.

     36. (with V.P. Maslov and G.B. Shpiz). Linear Functionals on
Idempotent Spaces: an Algebraic Approach// Doklady Mathematics,
v.58, # 3, 1998, p. 389-391. See E-print arXiv:math.FA/0012268 
.

     37. (with V.P. Maslov and A.N. Sobolevskii) Idempotent
Mathematics and Interval Analysis. - The Erwin Schroedinger
International Institute for Mathematical Physics, Vienna,
1998. See also E-print 1998 (http://www.esi.ac.at).

     38. (with V.P. Maslov and G.B. Shpiz) Tensor Products
of Idempotent Semimodules. An Algebraic Approach // Mathematical
Notes, v. 65, # 4, 1999, p. 479-489. See also E-print arXiv:
math.FA/0101153

     39. (with E.V. Maslova) Universal Numerical Algorithms
and Their Software Implementation // Programming and Computer
Software, v. 26, # 5, 2000, p. 275-280. See also E-print arXiv:
math.SC/0102114

     40. (with A.N. Sobolevskii) Exact Interval Solutions of
the Discrete Bellman Equation and Polynomial Complexity of 
Problems  in Interval Idempotent Linear Algebra // Doklady 
Mathematics, v. 62, # 2, 2000, p. 199-201. See also E-print 
arXiv:math.LA/0101041

     41.  (with  V.P.  Maslov  and  A.Ya.Rodionov) A Unifying
Approach   to  Software   and   Hardware  Design  for  Scientific
Calculations and Idempotent Mathematics. - International Sophus 
Lie Centre, Moscow 2000. See also E-print arXiv:math.SC/0101069 
.

     42. Numerical Mathematics Should Be Taught Differently. -
In: The 9th International Congress on Mathematical Education,
ICME-9. Topics Study Group 10. Trends in Mathematics and
Mathematical Sciences. Reflections on Mathematics Education.
August 1-2, 2000, Tokyo/Makuhari, p. 18-21.

     43. (with A.N. Sobolevskii) Idempotent Interval Analysis
and Optimization Problems // Reliable Computing, v. 7, # 5, 2001, 
p. 353-377. See also E-print arXiv:math.SC/0101080

     44. (with V.P. Maslov and G.B. Shpiz) Idempotent Functional
Analysis. An Algebraic Approach // Mathematical Notes, v. 69, 
# 5, 2001, p. 696-729. See also E-print arXiv:math.FA/0009128 
.

     45. (with V.P. Maslov and G.B. Shpiz) Nondigital
Implementations of the Arithmetic of Real Numbers by Means of
Quantum Computer Media // Mathematical Notes, v. 70, # 1, 2001,
p. 53-60. See also E-print arXiv:quant-ph/9904025

     46. (with V.P. Maslov and G.B. Shpiz) Idempotent (Asymptotic)
Analysis and the Representation Theory. - in: V.A. Malyshev and
A.M. Vershik (eds.), Asymptotic Combinatorics with Applications
to Mathematical Physics. - Kluwer Acad. Publ., Dordrecht et al.,
2002, p. 267-278. See also E-print arXiv:math.RT/0206025 
.

     47. (with G.B. Shpiz) Nuclear Semimodules and Kernel Theorems
in Idempotent Analysis: An Algebraic Approach//Doklady Mathematics,
v. 66, #2, 2002, p.197-199. See also E-print arXiv:math.FA/0202026 
.

     48. Error Autocorrection in Rational Approximation and Interval
Estimates//Central European Journal of Mathematics, V.1, #1, 2003.
E-print. See also E-print arXiv:math.NA/0207183

     49. Dequantization of Mathematics, idempotent semirings and
fuzzy sets. -- In: LINZ 2004. 25th Linz Seminar on Fuzzy Set Theory
"Mathematics of Fuzzy Systems". Linz, Austria, February 3 - 7, 2004/
E.P. Klements, E. Pap, Editors, Johannes Kepler Univ., Linz, 2004,
p. 113-117.

     50. (with V.P. Maslov, eds.)  Idempotent  Mathematics  and 
Mathematical Physics,  AMS  "Contemporary Mathematics", 2005.

     51. The Maslov Dequantization,Idempotent and Tropical 
Mathematics: A Very Brief Introduction  -- in [50], p. 1-17.
See also E-print arXiv:math.GM/0501038

     52. (with G.B. Shpiz) The  dequantization  transform  and 
generalized Newton polytopes. - In [50], 181-186. See also 
E-print arXiv:
math-ph/0412090

     53. (with G.B. Shpiz) Kernel  theorems  and nuclearity in 
idempotent  mathematics.  An  algebraic  approach,  Journal of 
Mathematical Sciences, v. 141, #4, 2007, p. 1417-1428. See also E-print arXiv:
math.FA/0609033

     54. The Maslov dequantization, idempotent and tropical 
mathematics: A brief introduction, Journal of Mathematical 
Sciences, v. 140, #3, 2007, p. 426-444. See also E-print arXiv:math.GM/
0507014

     55. (with G.B. Shpiz)  Engel  type  theorems  for 
representations of groups in idempotent spaces. - In preparation.

     56. Irreducible Representations of Complex and Real  
Nilpotent Lie Groups in Locally Convex Spaces. - In preparation.

     57. Lie Hypergroups and Their Representations. - 
In preparation.


                  BRIEF SUMMARY OF RESULTS

                  1. Representation Theory

     My papers  [5-11, 13, 16-19, 27, 46, 56] are devoted to
the theory of  representations of  Lie  groups  and  locally
compact groups (generally speaking, representations that are
infinite-dimensional and  not unitary).  The description  of
the group  representations reduced to the description of the
group algebras,  different group  algebras corresponding  to
different classes  of representations.  The  group  algebras
which I  have studied  are topological, and the study of the
representations of  these algebras  is  connected  with  the
study of  their closed  ideals, right,  left, and  two-sided
[6,16]. Completely  irreducible representations  of  complex
nilpotent Lie  groups with  holomorphic matrix elements were
studied. The  description of such representations reduced to
the  description   of  representation  of  a  special  group
algebra, the  algebra of  analytic  functionals.  Completely
irreducible (non-unitary)  representations of real nilpotent
Lie groups  were constructed  by using  the results obtained
[5]. A classification of all completely irreducible
representations of nilpotent Lie groups is obtained [5,16,56].
So the well-known A.A. Kirillov's problem is solved.
     Some results  about   spectral  analysis of arbitrary
representations of metabelian  groups  were presented [16].
The Laplace transform on  Lie  groups  was studied [7, 16].

     Using V.I.Lomonosov's  techniques  I  have  obtained  a
solution  of   M.A.Naimark's  problem   about  the  complete
irreducibility of  some representations  of  the  Heisenberg
group [19, theorem 6].

     Several approaches  to the  theory  of  characters  for
infinite-dimensional representations  of topological  groups
and algebras  were presented  in [8,  9, 13,  17, 19].  Some
sufficient   conditions    were   given    under   which   a
representation is  determined by  its character  up to  some
natural equivalence relation.

     In   [10,   27]  primary   decompositions   of   finite
dimensional representations  of Lie  algebras and Lie groups
(that are similar to decompositions of linear operators with
respect to  root subspaces)  were studied. In particular, we
have described  all the  Lie algebras for which each complex
representation admits such a decomposition.

     In  [46, 55]  representations  of  groups in idempotent
linear spaces  are  examined in the  framework of Idempotent
Mathematics.

                   2. Functional Analysis

     My papers  [3, 9,  11, 13,  17, 18, 21, 26] are closely
related  with   classical  problems   of  S.Banach   and  A.
Grothendieck (the  basis problem, the approximation problem,
the trace  problem, the  invariant subspace problem) for the
case of arbitrary locally convex spaces.

     In particular, the following results give a solution of
the   A.Grothendieck's    trace   problem    ("probleme  de
biunivocite").

     Theorem 1.  Any nuclear  operator in  a locally  convex
space  E   has  a   well-defined  trace   in  the  sense  of
Grothendieck if E has the approximation property.

     Theorem 2. There exists a quasi-complete locally convex
space with  the approximation  property in which one can not
define the trace for all Fredholm operators.

     Theorem 3.  Any Fredholm  operator in  a locally convex
space  E   has  a   well-defined  trace   in  the  sense  of
Grothendieck if E has the bounded approximation property.

     Theorem 4.  If E  is a locally convex space which has a
Schauder basis,  then every  nuclear operator  (or  Fredholm
operator) on  E has  a well-defined  matrix trace which does
not depend  on the  choice of  the basis, and coincides with
the trace in the sense of Grothendieck.

                   3. Hypergroups Theory

     My papers [12, 15 , 20, 24, 25, 32, 57] are devoted  to
the theory  of hypergroups.   Essential  fragments  of  this
theory became  familiar as the theory of the J.Delsarte-B.M.
Levitan generalized translation operators, the theory of the
Ju.M.Berezansky-S.G.Krein    hypercomplex    systems    with
continuous basis,  the theory  of convolution algebras, etc.
Roughly speaking,  a hypergroup  is a  topological space  or
manifold with  a supplementary  structure, which permits one
to construct  a Banach or topological algebra of the type of
a group  algebra - a hypergroup algebra. Thus, in the theory
of hypergroups,  just as  in the  theory of supergroups, the
object of  generalization is  not so much a group as a group
algebra (coalgebra). For some classes of hypergroups results
on a  connection with infinitesimal objects in the spirit of
the Lie theory are found, see [15]. The ideas and methods of
the theory of group representations carries over to the case
of  hypergroups,   while   it   is   convenient   to   treat
representations of  hypergroups as  representations  of  the
corresponding hypergroup algebras. In particular, in [12] an
abstract Plansherel  theorem  is  stated  and  an  inversion
formula is  given for  a broad  class  of  hypergroups  that
includes all locally compact groups. The theory of Lie
hypergroups, their Lie hyperalgebras and representations is
developed in [15, 24, 32].

Relations  to  Maslov's  canonical  operator  and  Integral
Geometry are discussed [32].


    4. Rational Approximations. Theory and Applications

     Methods  of   rational  approximations  of  real-valued
functions   were    investigated   and   implemented.   Some
paradoxical effects  occurring in  these approximations were
discovered and explained, see [2, 4, 14, 28, 29]. The nature
of one  of   them  is  the  following.  If  "good" method of
constructing  of   rational  approximations   is  used  (for
example, Pade  approximations, linear  and non-linear  Pade-
Chebyshev  approximations   etc.)  then   large  errors   in
calculated coefficients have no significant influence on the
overall precision  of approximation  constructed. Errors  of
numerator and  denominator cancel  each other. The reason of
this cancellation is that the errors of the coefficients are
not completely independent, but form coefficients of another
approximant  to  the  same  function.  Relations to interval
analysis are discussed [28, 48].

     Efficient algorithms  for calculation of functions were
designed and implemented for concrete small computers  (see,
e.g., [2, 29]).

                  5. Computer Technologies

     New computational  schemes and  algorithms for  decimal
computers were designed, see [2, 4, 29]. Several devices for
fast calculation of functions were invented. I was a manager
of several large software  projects.  I  didn't include  the
corresponding  papers  to  the  list  of  publications. Some
important applications of V.P. Maslov's  Idempotent Calculus
to hardware and software design are discussed in [30, 31, 33,
37, 39-43]. Quantum computing is discussed in [45].

                6. Idempotent Mathematics
      
    Idempotent Mathematics can be treated  as  a result of a 
dequantization of the traditional Mathematics as  the Planck 
constant  tends to zero  taking  pure imaginary values,  see
[30, 31, 44, 46, 51, 54].  For  example,  the field of  real 
numbers can be treated as a quantum object whereas idempotent 
semirings can be examined  as "classical" or "semiclassical" 
objects  (a semiring is called  idempotent  if the  semiring 
addition is idempotent, i.e. x + x = x). Idempotent Mathema-
tics  (in a  modern  sense)   was  founded  by  V.P.  Maslov  
and  his collaborators.

    In the spirit of N.Bohr's correspondence principle there 
is a (heuristic)  correspondence  between important, useful, 
and interesting  constructions  and  results over fields and 
similar  results  over  idempotent  semirings [30, 31].  For 
example,  the  superposition  principle in Quantum Mechanics 
(the linearity of the Schroedinger equation)  corresponds to  
a  linearity  of  the Hamilton-Jacobi and Bellman  equations 
over idempotent semirings.  A systematic application of this
correspondence  principle  leads  to  a variety  of  results 
including  such  exotic  applications  as  a methodology  to 
construct   computer   devices  (processors)  for  numerical 
calculations  and  to get the corresponding patents, as well
as a  methodology  for  software design see [30, 31, 39, 40, 
41, 42, 43]. 

    In the framework of Idempotent Mathematics a new version 
of Functional Analysis is developed from idempotent variants  
of  basic  theorems  (e.g.  of the Hahn-Banach type) to  the 
theory of  tensor products,  nuclear  operators and  nuclear 
spaces in  the spirit of  A. Grothendieck  as well as  basic 
concepts  and  results  of the theory  of  representation of 
groups in  idempotent  linear spaces [36, 38, 44, 46, 47, 51
-- 55].

         7. Mathematical Modeling and Optimization

     A new  method of  constructing analytical  models using
rational and spline approximations was designed. A number of
models were worked out for concrete users. Some of my papers
(which  I  didn't  include  to  the  list)  are  devoted  to
statistical models and methods.
     
     Many  algorithms,  software and hardware facilities for  
effective  solving   of  a  large  number  of  problems   in  
optimization  and  mathematical  modeling  were  constructed 
and examined [2, 4, 14, 30, 37, 39 - 43, 48].  An  essential  
aspect of this activity is developing a system of algorithms, 
utilities and programs based on a new mathematical  calculus  
which is called Idempotent Mathematics  (Idempotent Analysis  
or Idempotent Calculus), see [30, 31, 33, 36-44].

         8. Numerical Analysis and Interval Analysis

     Nonstandard  basic  numerical  algorithms   and   their 
implementations  for decimal computers were described in the
book [2] and in [29].  For example, all elementary functions
can be calculated  (for ordinal  or double precision)  using
a Jacobi fraction with a fixed number of parameters.

     Several  approximate  construction methods for rational
approximations  to functions and their computer realizations
were  developed  and  an effect of error autocorrection  was
discovered  and  formulated.  It was shown  that this effect
allows  us  to  control  calculation errors  by changing the
construction   procedure   depending  on  the  form  of  the 
corresponding approximant [4, 29]. Construction  methods for
linear and nonlinear  Pade-Chebyshev rational approximations
involving a computer algebra system were also described  [4,
14, 29].            

     A general form  of  the error autocorrection effect was
examined  and  it  was shown that in the case of this effect
all  the  standard  methods  of  "smooth"  interval analysis 
(including the so-called  a posteriori interval analysis  in 
the sense of Yu. Matiyasevich)  lead  to nonreasonable (very 
pessimistic) estimates.

     In the framework of Idempotent Mathematics a version of 
"nonsmooth"  interval analysis was developed  especially for
optimization problems [40, 43].  In this case  all estimates 
are exact  for algorithms  presented in terms  of Idempotent
Mathematics.  Interval solutions to a linear matrix equation
over  idempotent semirings  (the so-called  discrete Bellman
equation)  were  constructed  and  it  was  proved  that the 
computational  complexity  of  the problem is polynomial; in 
the  traditional  interval  analysis,  standard  problems of
linear algebra are NP-hard.


                                G.  L. Litvinov
                                 February 2007



                        PUBLICATIONS IN RUSSIAN (1-107)
                    (for publications in English see below)

     1. On  completely  irreducible representations of complex and real 
nilpotent Lie groups // Funktsional.  Analiz i ego Prilozhen., v. 3, # 4, 
1969, p. 87-88.
     2. Group algebras of analytic functionals and their representations // 
Doklady AN SSSR, v. 190, # 4, 1970, p. 769-771.
     3. On continuous representations of metabelian Lie groups  // Uspehi 
Matemat. Nauk, v. 26, # 4, 1971, p. 237-238.
     4. The Laplace transform on Lie groups // Funktsional. Analiz i ego 
Prilozhen., v. 6, # 1, 1972, p. 83-84.
     5. Representations of groups in  locally convex spaces and topological 
group algebras // Trudy  Semin. Vektor and Tenzor Anal., v. 16, 1972, 
p. 267-349.
     6. General concepts of Quantum Mechanics. - In: F.A.Berezin et al.,  
Lectures on Quantum Mechanics, Moscow State Univ., Dep. Math. Mech. Publ., 
1972, p. 5-44.
     7. (with M.A.Shubin) Operators in Hilbert space. Spectral theorems. 
Ibid., p. 222-262.
     8. Characters and simple representations // Doklady AN  SSSR, v. 214, 
# 3, 1974, p. 29-32.
     9. On traces of operators and characters of irreducible representations 
in  locally  convex spaces  //  Ibid.,  v.  214,  # 5, 1974, p. 1027-1030.
     10. On conditions under which a representation is determined by its 
character, up to equivalence // Trudy Semin. Vektor. And Tenzor. Anal., v. 17, 
1974, p. 325-349.
     11. (with B.G.Martynov) Textbook on Calculus, part 2. - Moscow, Eng. 
Acad. Publ., 1974. - 220 pp.
     12. (with M.S.Onuhov) Textbook on Calculus, part 3, Ibid., 1975. - 222 pp.
     13. (with N.A.Berezina) Mathematical Statistics Algorithms Collection. - 
All-Union State Institute for Statistics Technology Publ., 1975. - 19 pp.
     14. (with  G.A.Denisevich)  Statistical  data processing with 
minicomputers of the M5000 type // Vestnik Statistiki, 1976, # 9, p. 49 - 52.
     15. (with  G.A.Denisevich) Evaluation of small computers possibilities 
for data processing by means of mathematical methods. - In: Appendix to 
Proceedings of the Association of M5000 computers users, Dnepropetrovsk, 
1976, p. 22-28.
     16. (with  M.V.Dunskaya) Abstract Data Types, - Moscow, All-Union State 
Institute for Statistics Technology Publ., 1977. - 40 pp.
     17. (with M.V.Dunskaya) PVK M5000 (M5010) System Software Package for 
Statistical Data Analysis,  - Moscow,  All-Union State Institute for Statistics
Technology Publ., 1977. - 52 pp.
     18. Mathematical Statistics Software for ES EVM Computers, - Moscow, 
All-Union State Institute for Statistics Technology Publ., 1977. - 51 pp.
     19. (with   E.A.Dmitrieva   et   al.)  Standard  Mathematical Programs. 
Software  for  PVK  M5000.  -  Moscow,  All-Union  State Institute for 
Statistics Technology Publ., 1978. - 137 pp.
     20. On generalized translation operators and their representations  //  
Trudy Semin.  Vector.  Tenzor.  Anal.,  v.  18, 1978, p. 345-371.
     21. Double topological algebras and topological Hopf algebras  //  Ibid., 
p. 372-375.
     22. (with G.B.Shpiz) Primary decompositions of finite dimensional 
representations of Lie algebras  and  Lie  groups  // Funktsional. Analiz i 
ego Prilozhen., v. 12, # 2, 1978, p. 86-87.
     23. (with A.P.Kurantov  et  al.) Computer-aided  System  for Science and  
Technics Information based on the USSR State Archive Fund. Technical project. 
State registration number GR 77018384. - Moscow, VNIIDAD, 1978. - 502 pp.
     24. On traces of linear operators in locally convex spaces // Funktsional.
Analiz i ego Prilozhen., v. 13, # 1, 1979, p. 73-74.
     25. (with  G.B.Shpiz) Primary Decompositions of finite dimensional 
representations of Lie algebras and Lie groups // Trudy Semin. Vector. Tenzor. 
Anal., v. 19, 1979, p. 250-262.
     26. On  traces  of linear operators in locally convex spaces, Ibid., 
v. 19, 1979, p. 263-272.
     27. (with A.P.Kurantov  et  al.)  Computer-aided  System  for Science 
and  Technics Information based on the USSR State Archive Fund. Working 
project.  State registration number  GR  77018384. - Moscow, VNIIDAD, 
1979. - 1555 pp.
     28. (with  G.P.Galadzheva  and  E.A.Kondratyeva) Software for the 
computer-aided system ASNTI GAF SSSR  //  Express-information. Archives, 
1979, # 4 (Moscow, VNIIDAD Publ.), p. 13-17.
     29. (with G.P.Galadzheva,  V.G.Zinchenko)  Hardware  for  the 
computer-aided system ASNTI GAF SSSR // Ibid., p. 25-31.
     30. (with G.P.Galadzheva et al.) Interactive information system. -  
Proceedings  of the All-Union conference "Dialogue-79", Serpukhov, 1979, 
p. 213-215.
     31. Statistical  computer  data  processing.  - In:  Creation problems 
for the Computer-Aided Science and  Technics  Information System  based  on 
the USSR State Archive Fund.  - Moscow,  VNIIDAD Publ., 1981, p. 118-163.
     32. (with  M.V.Dunskaya) Abstract data types and their applications 
prospects. - Ibid., p. 164-208.
     33. (with  V.I.Lomonosov) Density theorems in locally convex spaces and 
their applications// Trudy Semin. Vektor. Tenzor. Anal., v. 20, 1981, p.210-227.
     34. (with B.M.Levitan) Generalized translation  operators. - In: 
Mathematical Encyclopedia, v. 3, - Moscow, Soviet Encyclopedia Publ., 1981, 
p. 1111-1116.
     35. (with  O.V.Golosov  et  al.) Technical Specifications for the ASNTI 
GAF SSSR system development.  State registration  number GR 77018384. - 
Moscow, VNIIDAD, 1981. - 22 pp.
     36. (with R.I.Tolstyh, L.I.Shadurskaya, E.A.Dmitrieva) Mathematical 
Algorithms and Programs for Small Computers. - Moscow, Finances and Statistics
Publ., 1981. - 112pp.
     37. (with  R.M.Borisyuk) Program implementation of elementary functions 
calculation algorithms for the "Mir" type computers. - In [36], Appendix, 
p. 103-109.
     38. Approximate construction of rational approximations.  In: XV Voronezh 
Winter Mathematical School. - Voronezh State University, 1981, p. 62-63.
     39. Organization of elementary functions computer calculation. - Ibid., 
p.64.
     40. Boolean algebras and automata. - In:  L.A.Basova et al., Lectures 
and Problems on Mathematics.  - Moscow,  Education Publ., 1981, p. 52-70.
     41. (with  L.I.Vainerman)  The  Plancherel  formula  and  the inversion 
formula for generalized translation operators // Doklady AN SSSR, v. 257, 
# 4, 1981, p. 792-795.
     42. (with V.I.Lomonosov) Density theorems in  locally  convex spaces and 
irreducible representations // Doklady AN SSSR, v. 257, # 4, 1981, p. 826-830.
     43. (with O.V.Golosov et al.) Basic System Analysis  for  the ASNTI GAF 
SSSR System. - Moscow, VNIIDAD, 1981. - 479 pp.
     44. (with N.A.Berezina et al.) Development of the  ASNTI  GAF SSSR System. 
-  In:  Proc. of  XII  sci.  seminar "GASNTI System Investigations", v. II, 
1981, p. 60-62.
     45. (with  A.P.Kurantov  et  al.)  Creation  and exploitation start of 
the  ASNTI  GAF  SSSR system. Final Report. State registration number GR 
7708384. - Moscow, VNIIDAD, 1981. - 48 pp.
     46. (with  G.P.Galadzheva  et  al.) Hardware and software for the ASNTI 
GAF SSSR  system.  -  In:  High  Efficiency  Systems  of Information Retrieval
and Data Base Management. - Proc. Of All-Union Symposium, - Kishinev, 1982, 
p. 43-56.
     47. (with  N.A.Berezina  et  al.)  Problems  and construction principles 
for the ASNTI GAF SSSR  system.  -  In:  Proc.  of  the All-Union Conference
"Problems  of  Information  Support for Fundamental and Applied Scientific 
Investigations after XXVI  KPSS Congress Solutions. (Zvenigorod, 4-6 May, 
1982)", v. 2. - Moscow, USSR Sci. Acad. Publ., 1982, p.123-125.
     48. (with I.A.Andreeva et al.) Dialogue tools development for the ASNTI 
GAF  SSSR system. In: Proceedings of the All-Union conference "Man-Machine 
Dialogue",  v.  1 - Leningrad, LIAP Publ., 1982, p.24-26.
     49. Approximation properties of locally convex spaces and the trace 
problem //  Teor. Funktsii, Funktsional. Anal. i Prilozhen., v. 39, 1983, 
p. 73-87.
     50. General concepts of quantum mechanics.  - In: F.A.Berezin et al.,  
The Schroedinger Equation.  - Moscow,  Moscow State Univ. Publ., 1983, p. 7-45.
     51. (with M.A.Shubin) Spectral theory of operators in Hilbert spaces. - 
In [49], Appendix 1, p. 294-366.
     52. (with  V.N.Friedman) Approximate construction of rational 
approximations //  Comptes Rendus  de  l'Academie Bulgare des Sciences, 
v. 36, # 1, 1983, p. 49-52.
     53. Software  for  the  ASNTI  GAF   SSSR   System.   -   In: Applications
of  System Analysis Methods to the ASNTI GAF SSSR system. - Moscow, VNIIDAD 
Publ., 1983, p. 132-150.
     54. (with I.A.Andreeva et al.) The publication  subsystem  of the  ASNTI 
GAF SSSR system.  - In:  Proc.  of the 4-d All-Union Conference "Problems of 
Computer-Aided Support for Processing  of Scientific and Technical  
Information", - Moscow, VIMI Publ., 1983, p. 35-37.
     55. (with  I.A.Andreeva  et  al.)  The  ASNTI GAF SSSR System Development. 
Technical project.  State  registration  number   GR 77018384. - Moscow, 
VNIIDAD, 1983. - 500 pp.
     56. (with  I.A.Andreeva  et  al.)  The  ASNTI GAF SSSR System Development. 
Working project.  State  registration  number GR 77018384. - Moscow, VNIIDAD, 
1984. - 980 pp.
     57. (with   I.A.Andreeva  et  al.)  Dialogue  preparation  of publications 
by means of the ASNTI GAF SSSR system. - In: Proc. Of the 3-d  All-Union 
�onference "Man-Computer Dialogue",  Serpukhov, 1984, p. 259.
     58. Calculation system for decimal computers.  - In: Personal Dialogue 
Systems  Based  on Microcomputers  (Personal Computers). Dialogue - 84 -  
Micro.  Proc.  All-Union  Conference. Leningrad, 19-22 November 1984. - 
Leningrad, "Nauka Publ.", 1984, p. 86-88.
     59. (with V.A.Sidorova) Problems of sample method applications for mass 
documentation analysis.  - Moscow,  VNIIDAD, 1984. - 31 pp.
     60. (with  I.A.Andreeva) Extended time standards for research tasks in 
VNIIDAD, - Moscow, VNIIDAD, 1985. - 55 pp.
     61. (with  I.A.Andreeva  et al.) PADE - Rational Approximants Calculation.
Description  and Program. - Pushchino, Research Computer Centre, Program 
Fund, 1985. - 33 pp.
     62. Fredholm kernel. - In: Mathematical Encyclopedia, v. 5. - Moscow, 
"Soviet Encyclopedia Publ.", 1985, p. 660.
     63. Nuclear C*-algebra.- Ibid., p. 1029.
     64. Nuclear bilinear form.- Ibid., p. 1029-1030.
     65. Nuclear norm.- Ibid., p. 1031-1032.
     66. Nuclear space.- Ibid., p. 1033-1037.
     67. Nuclear operator.- Ibid., p. 1037-1041.
     68. Kernel of an integral operator. - Ibid., p. 1042.
     69. Kernel of a linear operator. - Ibid., p. 1043.
     70. Problem oriented small computers and  information  arrays processing. 
- In:  Computer-Aided Document Information Processing. - Moscow, VNIIDAD, 
1985, p. 1-22.
     71. Singularities  of small computers software.  - Ibid.,  p. 23-46.
     72. (with  I.A.Andreeva  et  al.) Formation and processing of information 
arrays in the publication subsystem of the  ASNTI  GAF SSSR system.  - In: 
Proc. Semin. Computer-Aided Data Processing. - Moscow, VIMI Publ., 1985, 
p. 38-40.
     73. (with  I.A.Andreeva)  The  publication  subsystem  of the ASNTI GAF 
system // Express-information.  Archives; 1985, # 3 (35), p.1-12.
     74. Hypergroups   and   hypergroup  algebras.  -  In:  Modern Problems of 
Mathematics. Recent Achievements.  v.  25.  - Moscow, VINITI, 1985, p. 57-106.
     75. (with   A.P.Krukov,  A.Ya.Rodionov)  Application  of  the REDUCE  
system  to  rational approximants  construction.  -   In: "Analytical   
Computer  Calculations  and  their  Applications  in Theoretical Physics". 
Proc. Int. Conf. on Computer Algebra and its Applications in  Theoretical 
Physics. Dubna, 17-20 September, 1985. - OIYaI Publ., Dubna, 1985, p. 322-326.
     76. (with O.V.Golosov et al.) Development of  the  ASNTI GAF SSSR system.
Sci. report.   State   registration   number   GR 01822040055. - Moscow, 
VNIIDAD, 1985. - 78 pp.
     77. (with I.A.Andreeva  et  al.)  Standards  for  numbers  of employers 
in state archive institutions.  - Moscow, VNIIDAD, 1985. - 11 pp.
     78. (with  I.A.Andreeva  et  al.)  Standards  for  numbers of employers 
in central republican archive administrations. - Moscow, VNIIDAD, 1985. - 4 pp.
     79. (with I.A.Andreeva et al.) PADE -  rational  approximants calculation.
 -  In:  Information Catalogue  of  Program Tools in Program Fund of the USSR 
Sci.  Acad.  Research Computer Centre.  - Pushchino, NIVTs AN SSSR Publ., 
1985, p. 10-11; 1987, p. 11-12.
     80. (with I.A.Andreeva) SPLINE-PADE Program  System  and  its Applications
to Standards Development.  - Moscow, VNIIDAD, 1985. - 19 pp.
     81. (with  Ya.I.Fet) A device for function approximations.  - Soviet 
Patent # 1488838 with August 7,  1986  priority.  -  Moscow 1986, - 12 pp.; 
"Discoveries. Inventions". Official Bull., 1989, # 23, p. 234.
     82. (with   V.A.Komarov   et   al.)   Computer-Aided  Library Information 
System for VPTB (ASODI VPTB).  Technical Report, State registration number   
GR   01.87.0006435.  -  Moscow,  USSR  State Inventions and  Discoveries  
Committee,  All-Union  Patent   Techn. Library, 1987. - 70 pp.
     83. (with V.M.Zonov) Actual problems of artificial  intellect methods for 
computer input and transformation systems. - In: Proc. Semin. "Problems of 
Linguistic Technics  Development".  -  Moscow, "Lingvotekhnika Publ.", 1989, 
p. 40-45.
     84. Calculation organization method for decimal computers.  - Ibid., 
p. 46-53.
     85. Approximate construction of rational  approximations  and an effect 
of error autocorrection. - In: Mathematics and Modelling (A.D.Bazykin, Yu.G.
Zarkhin,  Eds).  -  Pushchino,  Sci.   Research Centre of the USSR Sci. Acad., 
1990, p. 99-141.
     86. (with V.P. Maslov) Idempotent Mathematics: correspondence principle 
and its computer applications // Uspekhi Matem. Nauk (Russian Matematicle 
Surveys), v. 51, # 6, 1996, p. 209-210.
     87. (with V.P. Maslov and G.B. Shpiz) Linear functionals on idempotent 
spaces: algebraic approach // Doklady Akademii Nauk (Doklady Mathematics), 
v. 363, # 3, 1998, p. 298-300.
     88. (with V.P. Maslov and G.B. Shpiz) Tensor products of idempotent 
semimodules. An algebraic approach // Matem. Zametki (Math. Notes), v. 65, 
# 4, 1999, p. 572-585.
     89. (with E.V. Maslova) Universal numerical algorithms and their 
software implementations // Programming, 2000, # 5, p. 53-62.
     90. (with E.V. Maslova) Universal algorithms and arbitrary precision 
calculations // Computational Technologies, v. 5, # 2, 2000, p. 68-70.
     91. (with V.P. Maslov) Idempotent Mathematics. - In: Modern Analysis 
and its Applications. Voronezh Winter Mathematical School, Voronezh: Voronezh 
State University, 2000, p. 20-22.
     92. (with I.A. Andreeva) Spaces of functions on smooth spaces, Ibid., 
p. 110-111.
     93. Universal algorithms and Idempotent Mathematics // Computer Tools 
in Educations, 2000#6, (St. Petersburg), p. 12-18.
     94. (with A.N. Sobolevskii) Exact interval solutions of the discrete 
Bellman equation and polynomial complexity of problems in interval idempotent 
linear algebra // Doklady Akademii Nauk (Doklady Math.), v. 374, # 3, 2000, 
p. 304-306.
     95. (with V.P. Maslov and A.N. Sobolevskii) Idempotent Mathematics and 
interval analysis // Computational Technologies, v. 6, # 6, 2001, p. 47-70.
     96. (with A.Ya. Rodionov and A.V. Churkin) Approximate rational arithmetic 
with controlled round off errors // Computational Technologies, v. 6, # 5, 
2001, p. 87-94.
     97. (with V.P. Maslov and G.B. Shpiz) Nondigital implementation of the 
arithmetic of real numbers by means of quantum computer media // Matem. Zametki 
(Math. Notes), v. 70, # 1, 2001, p. 59-67.
     98. (with V.P. Maslov and G.B. Shpiz) Idempotent functional analysis: 
an algebraic approach// Matem. Zametki  (Math. Notes), v. 69, # 5, 2001, 
p. 758-797.
     99. (with G.B. Shpiz) Nuclear Semimodules and Kernel Theorems in Idempotent
Analysis: An Algebraic Approach// Doklady Akademii Nauk, Vol. 386, # 3, 2002, 
p. 300-303.
     100. The Maslov dequantization and idempotent (tropical) mathematics. --
In : Voronezh Winter Mathematical School--2004, Voronezh State University,
Voronezh, 2004, p. 71-72.
     101. (with G.B. Shpiz) Dequantization and Newton polytopes. -- Ibid., 
p.114-115.
     102. (with G.B. Shpiz) Dequantization of mathematics and representations
of groups//Vestnik Tambovskogo Universiteta, ser. Estestvoznanie i 
tekhnicheskie nauki, Tambov, v. 10, #4, 2005, p.390-411.
     103. The Maslov dequantization, idempotent and tropical mathematics:
A brief introduction//Zapiski nauchnyh seminarov POMI, v. 326, 2005, 
p.145-182. E-print arXiv:math.GM/0507014
     104. (with A.N. Sobolevskii) Positive interval algorithms and idempotent
mathematics. -- In: Vserossijskoe (s mezhdunarodnym uchastiem) soveschanie
po interval'nomu analizu i ego prilozhenoyam "INTERVAL-06, July 1-4, 2006,
Peterhof, Russia. Extended abstracts. St. Petersburg, 2006, p. 72-74.
     105. (with G.B. Shpiz) Interval solutions of generalized algebraic 
equations in idempotent mathematics. -- Ibid., p.75-77.
     106. Kernel theorems and nuclearity in idempotent mathematics. An algebraic
approach//Zapiski nauchnyh seminarov POMI, v. 331, 2006, p. 60-83.
     107. Dequantization of mathematics. -- In: Globus: general-mathematical
seminar, Vol. 4. MCCME Publ., Moscow, in press.

                        PUBLICATIONS IN ENGLISH (108-186)
                    (for publications in Russian see above)

     1 (108).  On completely irreducible representations of complex and real 
nilpotent Lie groups// Functional Anal. Appl. v. 3, # 4, 1970, p. 332-334.
     2 (109).  Group algebras of analytic functionals and their representations 
// Soviet Math.  Dokl.,  v.  11,  # 1, 1970, p. 191-193.
     3 (110).  The Laplace transform on Lie  groups  //  Functional Anal. Appl.,
v. 6, # 2, 1972, p. 76,77.
     4 (111). Characters and simple representations // Soviet Math. Dokl., 
v. 15, # 1, 1974, p. 179-183.
     5 (112).  On Traces of operators and characters of irreducible 
representations in locally convex spaces // Soviet Math. Dokl., v. 15, # 1, 
1974, p. 308-312.
     6 (113).  (with  G.B.Shpiz)  Primary  decompositions of finite dimensional 
representations of Lie  algebras  and  Lie  groups  // Functional Anal. Appl., 
v. 12, # 2, 1978, p. 149-151.
     7 (114).  Traces of linear operators in locally convex spaces // 
Functional Anal. Appl. v. 13, # 1, 1979, p. 60-62.
     8 (115).  (with L.I.Vainerman) The Plansherel formula and  the inversion  
formula for generalized translation operators // Soviet Math. Dokl., v. 23, 
# 1, 1981, p. 333-337.
     9 (116).  (with  V.I.Lomonosov)  Density  theorems  in locally convex 
spaces and  irreducible  representations  //  Soviet  Math. Dokl., v. 23, # 2, 
1981, p. 372-375.
     10 (117). (with A.P.Kryukov and A.Ya.Rodionov) Construction of rational 
approximations by means of REDUCE.  - In:  Proceedings of the  1986  Symposium  
on  Symbolic  and   Algebraic   Computation. Symsac'86   (July   21-23,  1986,  
Waterloo,  Ontario),  Univ.  of Waterloo, 1986, p. 31-33.
     11 (118).  Hypergroups  and  hypergroup algebras // Journal of Soviet 
Math., v. 38, 1987, p. 1734-1761.
     12 (119).  Representations  of groups in locally convex spaces and 
topological group algebras // Selecta  Mathematica  Sovietica, v. 7, # 2, 1988, 
p. 101-182.
     13 (120).  On  conditions  under  which  a  representation  is determined
by  its  character,  up  to  equivalence  //  Selecta Mathematica Sovietica, 
v. 8, # 1, 1989, p. 73-97.
     14 (121).  On the traces of linear operators in locally convex spaces // 
Selecta Mathematica Sovietica,  v.  8,  #  3,  1989,  p. 203-212.
     15 (122).  (with V.I.Lomonosov) Density theorems  in  locally convex  
spaces and applications // Selecta Mathematica Sovietica, v. 8, # 4, 1989, 
p. 323-339.
     16 (123). Fredholm kernel. - Encyclopaedia of Mathematics, v. 4 - Kluwer 
Academic Publ., 1989, p. 103.
     17 (124).   (with   B.M.Levitan)   Generalized   displacement operators.  
- Encyclopaedia of Mathematics, v.4. - Kluwer Academic Publ., 1989, p. 224-228.
     18 (125).  Kernel of a linear operator.  -  Encyclopaedia of Mathematics,
v. 5. - Kluwer Academic Publ., 1990, p. 263.
     19 (126).  Kernel of an integral operator. - Encyclopaedia of Mathematics, 
v.5. - Kluwer Academic Publ., 1990, p. 265.
     20 (127).  Nuclear  bilinear   form.   -   Encyclopaedia   of Mathematics, 
v. 6. - Kluwer Academic Publ., 1990, p. 485.
     21 (128). Nuclear C*-algebra. - Encyclopaedia of Mathematics, v. 6. - 
Kluwer Academic Publ., 1990, p. 485-486.
     22 (129). Nuclear Norm. - Encyclopaedia of Mathematics, v. 6. - Kluwer 
Academic Publ., 1990, p. 486-487.
     23 (130).  Nuclear operator.  - Encyclopaedia of Mathematics,v. 6. - 
Kluwer Academic Publ., 1990, p. 487-490.
     24 (131).  Nuclear space.  - Encyclopaedia of Mathematics, v. 6. - Kluwer 
Academic Publ., 1990, p. 490-493.
     25 (132).  General  concepts  of  Quantum  Mechanics.  -  In: F.A.Berezin  
et  al.,  The Schroedinger Equation - Kluwer Academic Publ., Dordrecht/Boston/
London, 1991, p. 1-49.
     26 (133).  (with M.A.Shubin) Spectral theory of operators in Hilbert 
space.  -  In:  F.A. Berezin et al.,  The Schroedinger Equation. - Kluwer
Acad. Publ., Dordrecht/Boston/London, 1991, p. 386-465.
     27 (134). Generalized translation operators and their representations //
Selecta Mathematica  Sovietica,  v.  10,  #  4, 1991, p. 307-337.
     28 (135).  Double topological algebras and  topological  Hopf algebras // 
Selecta Mathematica Sovietica,  v.  10,  # 4, 1991, p. 339-343.
     29 (136).  Approximation  properties of locally convex spaces and the 
problem of uniqueness of the trace of a linear operator // Selecta Mathematica 
Sovietica, v. 11, # 1, 1992, p. 25-40.
     30 (137).  (with G.B.Shpiz) Primary decompositions of  finite dimensional  
representations  of  Lie  algebras  and Lie groups // Selecta Mathematica 
Sovietica, v. 11, # 1, 1992, p. 41-54.
     31 (138).  Error auto-correction in rational approximation. - In:  Proc.  
Intern. Conf. on Interval and Stochastic Methods in Science and Engineering
(Interval-92),  Moscow,  1992,  v.  2, p.59-63.
     32 (139). Error auto-correction in rational approximation // Interval
Computations, # 4(6), 1992, p. 14-18.
     33 (140).  On  Lie  hypergroups. - In: Abstracts Intern. Lie-Lobachevsky
Colloq. Tartu, October 26-30, 1992.
     34 (141). Error auto-correction in rational approximation. - In:  Intern.  
Congress  on  Computer  Systems  and   Applied Mathematics. CSAM'93. Abstracts. 
St. Petersburg, July 19-23, 1993. - Polylog Publ., St. Petersburg, 1993, 
p. 64-65.
     35 (142).  And the effect of error autocorrection.  - In:  A. Bazykin and 
Yu.  Zarkhin (Eds),  Mathematics and Modelling. - Nova Science Publ., New York, 
1993, p. 143-198.
     36 (143). Approximate construction of rational approximations and  an  
effect  of error autocorrection  //  Russian Journal of Mathematical Physics,  
v.  1, # 3, 1994, p. 313-352 (and preprint: Inst. Math., University of Oslo, 
# 8, May 1993 - 56 pp.) E-print arXiv:math.NA/0101042
     37 (144). (with V.P. Maslov and A.Ya. Rodionov) Unifying Approach to 
Software and Hardware Design for Scientific Calculations. International Sophus 
Lie Centre, Moscow, 1995. 
See also an updated e-version: E-print arXiv:quant-ph/9904024 v. 2
     38 (145).  (with V.P.  Maslov) Correspondence  principle  for Idempotent  
Calculus  and  some computer applications.  - Preprint IHES,  Bures-sur-Yvette, 
1995; the same in: Idempotency/J. Gunawardena (Ed.), Cambridge University 
Press, Cambridge, 1998, p. 420-443; E-print arXiv:math.GM/0101021
     39 (146). (with V.P. Maslov) Idempotent Mathematics: correspondence  
principle and applications//Russian Mathematical Surveys, v. 51, # 6, 1996, 
p. 1210-1211.
     40 (147). Interval computations and the effect of error auto-correction.
- In: Interval'96. International Conference on Interval Methods and Computer 
Aided Proofs in Science and Engineering, Sep. 30 - Okt. 2, 1996, Wuerzburg, 
Germany. Extended Abstracts. Wuerzburg, 1996, p. 76.
     41 (148). (with V.P. Maslov and A.Ya. Rodionov) Idempotent mathematics 
and scientific calculations, Ibid., p. 77-78.
     42 (149). Idempotent Algorithm. - Encyclopaedia of Mathematics, 
Supplemente Volume 1. - Kluwer Acad. Publ., 1997, p.312-313.
     43 (150). Idempotent Analysis. - Ibid, p. 313-315.
     44 (151). Idempotent Correspondence Principle. - Ibid, p. 315-316.
     45 (152). Idempotent semiring. - Ibid, p. 316.
     46 (153). Idempotent superposition principle. - Ibid, p. 317.
     47 (154). (with V.M. Tulovsky) Generalized Fourier Transform, Maslov's 
Canonical Operator and Hypergroups. - International Sophus Lie Centre, 
Moscow, 1997.
     48 (155). (with B. Komrakov, I. Krasil'shchik, and A. Sossinsky, Editors) 
Lie Groups and Lie Algebras, Their Representations, Generalizations, and 
Applications. - Kluwer Acad. Publ., Dordrecht et al., 1998.
     49 (156). (with K.A. Ross et al., editors) Harmonic Analysis and 
Hypergroups ("Trends in Mathematics" series) - Birkhauser, 1998.
     50 (157). (with V.P. Maslov and G.B. Shpiz) Linear functionals on 
idempotent spaces: an algebraic approach // Doklady Mathematics,  v. 58, # 3, 
1998, p. 389-391. E-print arXiv:math.FA/0012268
     51 (158). (with V.P. Maslov and A.N. Sobolevskii) Idempotent Mathematics 
and Interval Analysis. - The Erwin Schroedinger International Institute for 
Mathematical Physics, Vienna, 1998, . E-print arXiv:math.NA/9911126
(see also http://www.esi.ac.at).
     52 (159). (with V.P. Maslov and G.B. Shpiz) Idempotent Mathematics - In: 
International Conference Dedicated to the 90th Anniversary of L.S. Pontryagin. 
Abstracts. Algebra, Geometry and Topology. August, 31 - September, 6, 1998, 
Moscow. Steklov Mathematical Institute and Moscow State (Lomonosov) University, 
Moscow, 1998, p. 38-39.
     53 (160). (with V.P. Maslov and G.B. Shpiz) Tensor products of idempotent 
semimodules. An algebraic approach // Mathematical  Notes, v. 65, # 4, 1999, 
p. 479-489. E-print arXiv:math.FA/0101153
     54 (161). (with E.V. Maslova) Universal numerical algorithms and their 
software implementation // Programming and Computer Software, v. 26, # 5, 2000, 
p. 275-280. E-print arXiv:math.SC/0102114
     55 (162). (with A.N. Sobolevskii) Universal algorithms, idempotent  
mathematics, and interval solutions of optimization problems. - In: 6th 
International IMACS Conference on Applications of Computer Algebra, June 25-28,
2000, St. Petersburg, Russia. Abstracts. - Euler Institute and IMACS, St. 
Petersburg, 2000, p. 84-85.
     56 (163). (with V.P. Maslov) Idempotent Mathematics and Optimization. - 
In: 11th IFAC International Workshop "Control Applications of Optimization", 
CAO'2000, July 3-6, 2000, St. Petersburg, Russia. Abstracts. St. Petersburg, 
2000, p. 144-145. 
     57 (164). (with A.N. Sobolevskii) Idempotent interval analysis, matrix 
algebra, and optimization on graphs, Ibid, p. 242-243.
     58 (165). (with A.N. Sobolevskii) Exact interval solutions of the discrete
Bellman equation and polynomial complexity of problems in interval idempotent 
linear algebra // Doklady Mathematics, v. 62, # 2, 2000, p. 199-201. 
E-print arXiv:math.LA/0101041
     59 (166).  (with  V.P.  Maslov  and  A.Ya.Rodionov) A unifying approach   
to software and hardware design  for  scientific calculations and idempotent 
mathematics. - International Sophus Lie Centre, Moscow 2000. 
E-print arXiv:math.SC/0101069
     60 (167). (with A.Ya. Rodionov and A.V. Churkin) Approximate rational 
arithmetics and arbitrary precision calculations. - International Sophus Lie 
Centre, Moscow, 2000. E-print arXiv:math.NA/0101152
     61 (168). Numerical mathematics should be taught differently. - In: 
The 9th International Congress on Mathematical Education, ICME-9. Topics Study 
Group 10. Trends in Mathematics and Mathematical Sciences. Reflections on 
Mathematics Education. August 1-2, 2000, Tokyo/ Makuhari, p. 18-21.
     62 (169). (with A.N. Sobolevskii) Idempotent interval analysis and 
optimization problems // Reliable Computing, v. 7, # 5, 2001, p. 353-377. 
E-print arXiv:math.SC/0101080
     63 (170). (with V.P. Maslov) Idempotent Mathematics and Mathematical 
Physics. - In: International Workshop "Topology, Analysis and Related Topics. 
Moscow State University, August 29-31, 2001". Moscow, 2001, p. 13.
     64 (171). (with V.P. Maslov and G.B. Shpiz) Idempotent functional analysis.
An algebraic approach // Mathematical Notes, v. 69, # 5, 2001, p. 696-729. 
E-print arXiv:math.FA/0009128
     65 (172). (with V.P. Maslov and G.B. Shpiz) Nondigital implementations of 
the arithmetic of real numbers by means of quantum computer media // 
Mathematical Notes, v. 70, # 1, 2001, p. 53-60. E-print arXiv:quant-ph/9904025 
     66 (173). (with V.P. Maslov and G.B. Shpiz) Idempotent (Asymptotic) 
Analysis and the Representation Theory. - In: V.A. Malyshev and A.M. Vershik 
(eds.), Asymptotic Combinatorics with Applications to Mathematical Physics. 
Kluwer Academic Publishers, Dordrecht et al, 2002, p. 267-278. 
E-print arXiv:math.RT/0206025
     67 (174). (with G.B. Shpiz) Nuclear Semimodules and Kernel Theorems in 
Idempotent Analysis: An Algebraic Approach/Doklady Mathematics, Vol. 66, # 2, 
2002, p. 197-199. E-print arXiv:math.FA/0202026
     68 (175). Error Autocorrection in Rational Approximation and Interval 
Estimates//Central European Journal of Mathematics, Vol. 1, # 1, 2003, p. 36-60.
See also math.NA/0207183
     69 (176) (with M.I. Graev) Generalized Fourier Transforms and Hypergroups, 
generated by Problems of Integral Geometry. - In: Intern. Conf. KOLMOGOROV and 
CONTEMPORARY MATHEMATICS, Moscow, June 16-21, 2003. Abstracts. Moscow State 
University and Russian Acad. Sci., Moscow, 2003, p. 172-173.
     70. (177) Dequantization of Mathematics, idempotent semirings and fuzzy
sets -- In: LINZ 2004. 25th Linz Seminar on Fuzzy Set Theory "Matematics of
Fuzzy Systems". Linz, Austria, February 3-7, 2004. Abstracts/E.P. Klements,
E. Pap, Editors, Johannes Kepler Univ., Linz, 2004, p. 113-117.
     71. (178) The Maslov dequantization, idempotent and tropical mathematics.
 -- In: Intern. Conf. "Topology, Analysis and Applications to Mathematical
Physics. Moscow, 14-18 February, 2005. Abstracts", Moscow State University,
Moscow, 2005, p.43-44.
     72. (179) (with G.B. Shpiz) Representation of groups in idempotent spaces:
an algebraic approach. -- In: Int. Conf. "Representation Theory, Dynamical 
Systems, and Asymptotic Combinatorics. St. Ptersburg, Russia, June 8-13, 2004".
Abstracts of talks, St. Ptersburg, Euler Intern. Math. Inst., 2004, p. 15-16.
     73. (180) (with V.P. Maslov, eds.) Idempotent Mathematics and Mathematical
Physics.  Contemporary Mathematics, Vol. 377. Amer. Math. Soc., Providence,
Rhode Island, 2005. - 370 pp.
     74. (181) The Maslov dequantization, idempotent and tropical mathematics:
a very brief introduction. -- Ibid., p.1-17. E-print arXiv:math.GM/0501038 
     75. (182) (with G.B. Shpiz) The dequantization transform and generalized
Newton polytopes. -- Ibid., p. 181-186. E-print arXiv:math-ph/0412090
     76. (183) (with G.B. Shpiz) Dequantization of mathematics and 
representations of groups. -- In: Intern. Conf. "Harmonic Analysis on 
Homogeneous Spaces, Representations of Lie groups and Quantization. 
April 25-29", 2005. Abstracts. Tambov State University, Tambov, 2005, p. 15.
     77. (184) (with V.P. Maslov and G.B. Shpiz) Dequantization, logic, and
fuzzy sets. -- In: Intern. Conf. "Methods of Logic in Mathematics. July 18-14,
2005". Program. Abstracts. Euler Intern. Math. Inst., St. Petersburg, 2005, 
p.27-28.
     78. (185) (with G.B. Shpiz) Kernel theorems and nuclearity in idempotent
mathematics. An algebraic approach, Journal of Mathematical Sciences, v. 141, 
#4, 2007, p. 1417-1428. E-print arXiv:math.FA/0609033
     79. (186) The Maslov dequantization, idempotent and tropical mathematics:
A brief introduction, Journal of Mathematical Sciences, v. 140, #3, 2007,
p.426-444.  E-print arXiv:math.GM/0507014
    80. (187) (with G.B. Shpiz) The Maslov dequantization, convex geometry and 
linear operators. -- In : International Conference "OPERATOR ALGEBRAS AND TOPOLOGY",
Moscow, January 29 - February 03, 2007. Abstracts. Moscow, Moscow State University,
2007, p. 21-22.

Last modified: Sat Mar 31 23:22:24 MSK 2007