Shavgulidze, Evgeni Tengizovich

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Total publications: 31
Scientific articles: 27
Presentations: 4

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Doctor of physico-mathematical sciences (1991)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 30.11.1950
Keywords: functional integrals; quasi-invariant measures; groups of diffeomorphisms; representation of infinintly dimensional groups.


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.


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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. V. Belokurov, E. T. Shavgulidze, “Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics”, TMF, 200:3 (2019),  465–477  mathnet  elib; Theoret. and Math. Phys., 200:3 (2019), 1324–1334  isi  scopus
2. V. V. Belokurov, E. T. Shavgulidze, “Nonlinear nonlocal substitutions in functional integrals”, Fundam. Prikl. Mat., 21:5 (2016),  47–59  mathnet
3. 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, 2,  9–14  mathnet  mathscinet; Moscow University Mathematics Bulletin, 69:2 (2014), 51–55  scopus
4. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:5 (2004), 982–983  isi  scopus
5. S. S. Akbarov, E. T. Shavgulidze, “Two classes of spaces reflexive in the sense of Pontryagin”, Mat. Sb., 194:10 (2003),  3–26  mathnet  mathscinet  zmath  elib; Sb. Math., 194:10 (2003), 1427–1449  isi  scopus
6. 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  mathnet  mathscinet  zmath; Math. Notes, 68:1 (2000), 22–31  isi
7. 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  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 123:3 (2000), 792–800  isi
8. I. G. Tsar'kov, E. T. Shavgulidze, “Smooth Isometric Immersions into the Infinite-Dimensional Sphere”, Funktsional. Anal. i Prilozhen., 33:3 (1999),  93–95  mathnet  mathscinet  zmath; Funct. Anal. Appl., 33:3 (1999), 239–240  isi
9. 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  mathnet  mathscinet  zmath
10. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:3 (1999), 626–627  isi  scopus
11. 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, 6,  19–25  mathnet  mathscinet  zmath
12. 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  mathnet  mathscinet  zmath
13. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:2 (1997), 392–393  isi
14. E. T. Shavgulidze, “Quasi-invariant measures on groups of diffeomorphisms”, Tr. Mat. Inst. Steklova, 217 (1997),  189–208  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 217 (1997), 181–202
15. 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  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 109:1 (1996), 1294–1301  isi
16. 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  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 109:1 (1996), 1287–1293  isi
17. 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  mathnet  mathscinet  zmath; Theory Probab. Appl., 37:2 (1993), 402–404
18. S. A. Bogatyi, E. T. Shavgulidze, “Periodic points of a map of a system of intervals”, Mat. Zametki, 43:3 (1988),  365–381  mathnet  mathscinet  zmath; Math. Notes, 43:3 (1988), 210–219  isi
19. E. T. Shavgulidze, “A class of selfadjoint operators connected with the $P(\varphi)_n$ model”, Dokl. Akad. Nauk SSSR, 294:6 (1987),  1349–1353  mathnet  mathscinet
20. E. T. Shavgulidze, “Hahn–Jordan decomposition for smooth measures”, Mat. Zametki, 30:3 (1981),  439–442  mathnet  mathscinet  zmath; Math. Notes, 30:3 (1981), 710–712  isi
21. E. T. Shavgulidze, “On a diffeomorphism of a locally convex space”, Uspekhi Mat. Nauk, 34:5(209) (1979),  231–232  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:5 (1979), 245–246
22. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 12:3 (1978), 203–207
23. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 11:1 (1977), 82–83
24. E. T. Shavgulidze, “The Minlos theorem for measures that are not sign-definite”, Uspekhi Mat. Nauk, 31:3(189) (1976),  222  mathnet  mathscinet  zmath
25. E. T. Shavgulidze, “$B_r$ completeness”, Funktsional. Anal. i Prilozhen., 9:4 (1975),  95–96  mathnet  mathscinet  zmath; Funct. Anal. Appl., 9:4 (1975), 363–364
26. E. T. Šavgulidze, “Certain properties of fully complete locally convex spaces”, Tr. Mosk. Mat. Obs., 32 (1975),  251–266  mathnet  mathscinet  zmath
27. E. T. Shavgulidze, “On the hypercompleteness of locally convex spaces”, Mat. Zametki, 13:2 (1973),  297–302  mathnet  mathscinet  zmath; Math. Notes, 13:2 (1973), 180–182

28. 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  mathnet  elib; Russian Math. Surveys, 74:4 (2019), 771–773
29. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 64:1 (2009), 183–185  isi
30. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:5 (2004), 941–947  isi
31. 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, 5,  69–70  mathnet  mathscinet

Presentations in Math-Net.Ru
1. Полярное разложение меры Винера
E. T. Shavgulidze
Infinite dimensional analysis and mathematical physics
April 22, 2019 18:30
2. SYK-модель и интегралы Шварца
E. T. Shavgulidze
Infinite dimensional analysis and mathematical physics
November 20, 2017 18:30
3. О некоторых свойствах квазиинвариантных мер, групп диффеоморфизмов
E. T. Shavgulidze
Infinite dimensional analysis and mathematical physics
November 7, 2016 18:30
4. Representations of regularized traces and determinants in the functional integrals
O. G. Smolyanov, E. T. Shavgulidze
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 9, 2011 12:15

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