functional analysis, idempotent and tropical mathematics, representations of Lie groups, hypergroups, rational approximations, interval analysis, numerical methods, computer technologies.
UDC:
517.9, 517.958:530.145, 514.84
Subject:
Functional analysis, idempotent and tropical mathematics, representations of Lie groups, hypergroups, rational approximations, interval analysis, numerical methods, computer technologies.
Main publications:
G. L. Litvinov, “Representation of groups in locally convex spaces and topological group algebras”, Selecta Math. Sovietica, 7:2 (1988), 101–182
G. L. Litvinov, “Hypergroups and hypergroup algebras”, Journal of Soviet Math., 38 (1987), 1734–1761
G. L. Litvinov, “Approximation properties of locally convex spaces
and the problem of uniqueness of the trace of a linear operator”, Selecta Math. Sov., 11:1 (1992), 25–40
G. L. Litvinov, “Error autocorrection in rational approximations and interval estimates”, E-print journal, Central European Journal of Mathematics, 1:1 (2003), 36–60
G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, Journal of Mathematical Sciences, 140:3 (2007), 426–444
G. L. Litvinov, А. Ya. Rodionov, S. Sergeev, A. N. Sobolevski, “Universal algorithms for solving discrete stationary Bellman equations”, Russian Universities Reports. Mathematics, 24:128 (2019), 393–431
2014
2.
B. Kh. Kirshtein, G. L. Litvinov, “Analyzing stable regimes of electrical power systems and tropical geometry of power balance equations over complex multifields”, Avtomat. i Telemekh., 2014, 10, 110–124; Autom. Remote Control, 75:10 (2014), 1802–1813
2006
3.
G. L. Litvinov, G. B. Shpiz, “Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach”, Zap. Nauchn. Sem. POMI, 331 (2006), 60–83; J. Math. Sci. (N. Y.), 141:4 (2007), 1417–1428
2005
4.
G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, Zap. Nauchn. Sem. POMI, 326 (2005), 145–182; J. Math. Sci. (N. Y.), 140:3 (2007), 426–444
2001
5.
G. L. Litvinov, V. P. Maslov, G. B. Shpiz, “Nondigital Implementation of the Arithmetic of Real Numbers”, Mat. Zametki, 70:1 (2001), 59–67; Math. Notes, 70:1 (2001), 53–60
6.
G. L. Litvinov, V. P. Maslov, G. B. Shpiz, “Idempotent Functional Analysis: An Algebraic Approach”, Mat. Zametki, 69:5 (2001), 758–797; Math. Notes, 69:5 (2001), 696–729
1999
7.
G. L. Litvinov, V. P. Maslov, G. B. Shpiz, “Tensor products of idempotent semimodules. An algebraic approach”, Mat. Zametki, 65:4 (1999), 573–586; Math. Notes, 65:4 (1999), 479–489
1996
8.
G. L. Litvinov, V. P. Maslov, “Idempotent mathematics: a correspondence principle and its applications to computing”, Uspekhi Mat. Nauk, 51:6(312) (1996), 209–210; Russian Math. Surveys, 51:6 (1996), 1210–1211
1985
9.
G. L. Litvinov, “Hypergroups and hypergroup algebras”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 26 (1985), 57–106; J. Soviet Math., 38:2 (1987), 1734–1761
1981
10.
G. L. Litvinov, V. I. Lomonosov, “Density theorems in locally convex spaces and irreducible representations”, Dokl. Akad. Nauk SSSR, 257:4 (1981), 826–830
11.
L. I. Vainerman, G. L. Litvinov, “The Plancherel formula and the inversion formula for generalized translation operators”, Dokl. Akad. Nauk SSSR, 257:4 (1981), 792–795
1979
12.
G. L. Litvinov, “Traces of linear operators in locally convex spaces”, Funktsional. Anal. i Prilozhen., 13:1 (1979), 73–74; Funct. Anal. Appl., 13:1 (1979), 60–62
1978
13.
G. L. Litvinov, G. B. Shpiz, “Primary decompositions of finite-dimensional representations of Lie algebras and Lie groups”, Funktsional. Anal. i Prilozhen., 12:2 (1978), 86–87; Funct. Anal. Appl., 12:2 (1978), 149–151
1974
14.
G. L. Litvinov, “On traces of operators and characters of irreducible representations in locally convex spaces”, Dokl. Akad. Nauk SSSR, 214:5 (1974), 1027–1030
15.
G. L. Litvinov, “Characters and simple representations”, Dokl. Akad. Nauk SSSR, 214:3 (1974), 509–512
1972
16.
G. L. Litvinov, “The Laplace transform on Lie groups”, Funktsional. Anal. i Prilozhen., 6:1 (1972), 83–84; Funct. Anal. Appl., 6:1 (1972), 76–77
1971
17.
G. L. Litvinov, “The continuous representations of metabelian Lie groups in locally convex spaces”, Uspekhi Mat. Nauk, 26:4(160) (1971), 237–238
1970
18.
G. L. Litvinov, “Group algebras of analytic functionals, and their representations”, Dokl. Akad. Nauk SSSR, 190:4 (1970), 769–771
1969
19.
G. L. Litvinov, “On completely irreducible representations of complex and real nilpotent Lie groups”, Funktsional. Anal. i Prilozhen., 3:4 (1969), 87–88; Funct. Anal. Appl., 3:4 (1969), 332–334
2008
20.
A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh, “Mark Iosifovich Graev (to his 85th brithday)”, Uspekhi Mat. Nauk, 63:1(379) (2008), 169–182; Russian Math. Surveys, 63:1 (2008), 173–188
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