functional integrals; quasi-invariant measures; groups of diffeomorphisms; representation of infinintly dimensional groups.
Subject:
Construction of quasi-invariant measures on groups of diffeomorphismes of riemannian manifolds. Research of unitary represantations of groups of diffeomorphismes. Research of relations of different definitions of functional integrals. Proofs of theorem of Minlos for measures with alternating signs and theorem of Hahn–Jordan for smooth measures. Establishment of criterions of different species of completeness for locally convex spaces.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1973 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1978. D.Sci. thesis was defended in 1991. A list of my works contains more than 60 titles. Since 1979 I and O. G. Smolyanov have led the research seminar at MSU on infinite-dimensional analysis.
Main publications:
Shavgulidze E. T. Mesures quasi-invariantes sur les groupes de diffeomorphismes des varietes riemaniennes // C.R.Acad.Sci.Paris. 1995. T. 321. Serie I. P. 229–232.
Shavgulidze E. T. Some Properties of Quasi–invariant Measures on Groups of Diffeomorphisms of the Circle // Russian Journal of Mathematical Physics, 2000, v. 7, no. 4, p. 462–472.
V. V. Belokurov, E. T. Shavgulidze, “Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics”, TMF, 200:3 (2019), 465–477; Theoret. and Math. Phys., 200:3 (2019), 1324–1334
V. V. Belokurov, E. T. Shavgulidze, “Nonlinear nonlocal substitutions in functional integrals”, Fundam. Prikl. Mat., 21:5 (2016), 47–59; J. Math. Sci., 248:5 (2020), 544–552
S. B. Gashkov, E. T. Shavgulidze, “Representation of monomials as a sum of powers of linear forms”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 2, 9–14; Moscow University Mathematics Bulletin, 69:2 (2014), 51–55
Yu. P. Solov'ev, V. V. Belokurov, E. T. Shavgulidze, “The existence of functional integrals in a model of quantum field theory on a loop space”, Uspekhi Mat. Nauk, 59:5(359) (2004), 163–164; Russian Math. Surveys, 59:5 (2004), 982–983
S. S. Akbarov, E. T. Shavgulidze, “Two classes of spaces reflexive in the sense of Pontryagin”, Mat. Sb., 194:10 (2003), 3–26; Sb. Math., 194:10 (2003), 1427–1449
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “A method of summation of divergent series to any accuracy”, Mat. Zametki, 68:1 (2000), 24–35; Math. Notes, 68:1 (2000), 22–31
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory”, TMF, 123:3 (2000), 452–461; Theoret. and Math. Phys., 123:3 (2000), 792–800
I. G. Tsar'kov, E. T. Shavgulidze, “Smooth Isometric Immersions into the Infinite-Dimensional Sphere”, Funktsional. Anal. i Prilozhen., 33:3 (1999), 93–95; Funct. Anal. Appl., 33:3 (1999), 239–240
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “A general approach to calculation of functional integrals and summation of divergent series”, Fundam. Prikl. Mat., 5:2 (1999), 363–383
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “A summation method for divergent series”, Uspekhi Mat. Nauk, 54:3(327) (1999), 153–154; Russian Math. Surveys, 54:3 (1999), 626–627
E. T. Shavgulidze, “Quasiinvariant measures with respect to groups of diffeomorphisms on spaces of curves and surfaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 6, 19–25
1997
13.
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Calculation of functional integrals with the help of convergent series”, Fundam. Prikl. Mat., 3:3 (1997), 693–713
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Perturbation theory with convergent series for functional integrals with respect to the Feynman measure”, Uspekhi Mat. Nauk, 52:2(314) (1997), 155–156; Russian Math. Surveys, 52:2 (1997), 392–393
E. T. Shavgulidze, “Quasi-invariant measures on groups of diffeomorphisms”, Trudy Mat. Inst. Steklova, 217 (1997), 189–208; Proc. Steklov Inst. Math., 217 (1997), 181–202
E. T. Shavgulidze, “Special selfadjoint extensions of Schrödinger differential operators by means of Feynman integrals”, Dokl. Akad. Nauk, 348:6 (1996), 743–745
17.
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Method of approximate calculating path integrals by using perturbation theory with convergent series. II. Euclidean quantum field theory”, TMF, 109:1 (1996), 60–69; Theoret. and Math. Phys., 109:1 (1996), 1294–1301
V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Method of approximate calculating path integrals by using perturbation theory with convergent series. I”, TMF, 109:1 (1996), 51–59; Theoret. and Math. Phys., 109:1 (1996), 1287–1293
O. G. Smolyanov, E. T. Shavgulidze, “The support of a symplectic Feynman measure and the uncertainty
principle”, Dokl. Akad. Nauk, 323:6 (1992), 1038–1042; Dokl. Math., 45:2 (1992), 492–496
20.
O. G. Smolyanov, E. T. Shavgulidze, “A Simple Proof of Tarieladze's Theorem on Sufficiency of Positively Sufficient Topologies”, Teor. Veroyatnost. i Primenen., 37:2 (1992), 421–424; Theory Probab. Appl., 37:2 (1993), 402–404
O. G. Smolyanov, E. T. Shavgulidze, “Representation of the solutions of second-order linear evolution
superdifferential equations by path integrals”, Dokl. Akad. Nauk SSSR, 309:3 (1989), 545–550; Dokl. Math., 40:3 (1990), 552–557
E. T. Shavgulidze, “A measure that is quasi-invariant with respect to the action of a
group of diffeomorphisms of a finite-dimensional manifold”, Dokl. Akad. Nauk SSSR, 303:4 (1988), 811–814; Dokl. Math., 38:3 (1989), 622–625
O. G. Smolyanov, E. T. Shavgulidze, “The Fourier transform and pseudodifferential operators in
superanalysis”, Dokl. Akad. Nauk SSSR, 299:4 (1988), 816–820; Dokl. Math., 37:2 (1988), 476–481
S. A. Bogatyi, E. T. Shavgulidze, “Periodic points of a map of a system of intervals”, Mat. Zametki, 43:3 (1988), 365–381; Math. Notes, 43:3 (1988), 210–219
1987
25.
E. T. Shavgulidze, “A class of selfadjoint operators connected with the $P(\varphi)_n$ model”, Dokl. Akad. Nauk SSSR, 294:6 (1987), 1349–1353
E. T. Shavgulidze, “On a diffeomorphism of a locally convex space”, Uspekhi Mat. Nauk, 34:5(209) (1979), 231–232; Russian Math. Surveys, 34:5 (1979), 245–246
E. T. Shavgulidze, “An example of a measure quasi-invariant under the action of the diffeomorphism group of the circle”, Funktsional. Anal. i Prilozhen., 12:3 (1978), 55–60; Funct. Anal. Appl., 12:3 (1978), 203–207
E. T. Shavgulidze, “Conditions for certain forms of completeness in the class of projective limits of sequences of inductive limits of sequences of Fréchet spaces”, Funktsional. Anal. i Prilozhen., 11:1 (1977), 91–92; Funct. Anal. Appl., 11:1 (1977), 82–83
V. I. Bogachev, I. V. Volovich, B. S. Kashin, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. Yu. Khrennikov, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 80th birthday)”, Uspekhi Mat. Nauk, 74:4(448) (2019), 191–193; Russian Math. Surveys, 74:4 (2019), 771–773
2009
35.
V. I. Bogachev, V. S. Vladimirov, I. V. Volovich, B. S. Kashin, A. I. Kirillov, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. V. Uglanov, A. Yu. Khrennikov, A. M. Chebotarev, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 70th birthday)”, Uspekhi Mat. Nauk, 64:1(385) (2009), 175–177; Russian Math. Surveys, 64:1 (2009), 183–185
2004
36.
V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Uspekhi Mat. Nauk, 59:5(359) (2004), 135–140; Russian Math. Surveys, 59:5 (2004), 941–947
V. S. Vladimirov, V. A. Sadovnichii, P. L. Ul'yanov, R. A. Minlos, V. I. Bogachev, A. M. Stepin, A. V. Uglanov, E. T. Shavgulidze, “Oleg Georgievitch Smolyanov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, no. 5, 69–70
Feynman Integrals in Quantum Gravity E. T. Shavgulidze III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 8, 2023 10:55
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