Smolyanov, Oleg Georgievich

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Total publications: 76
Scientific articles: 74
Presentations: 29

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Abstract pages:20732
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Doctor of physico-mathematical sciences (1984)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Keywords: infinite dimensional analysis, topological vector spaces, stochastic analysis on Riemannian manifolds, Feynman path integrals, infinite dimensional Hamilton-Dirac systems, quantum information, open quantum systems, Schroedinger–Belavkin stochastic equations, measures on infinite dimensional manifolds, superanalysis, nonstandard analysis.


Some basic problems related to closed graph theorems and, in general, to homological properties of locally convex spaces, which attracted the experts at the beginning of 70-th, were solved. Those problems tracing back to Dieudonne, L. Schwartz, Grothendieck, Koethe, Ptak, Kelley, Raikov were already 15–20 years old that time. In particular it has been constructed a quotient of the space $D(R)$ which is isomorphic to a proper dense subspace of $R^\infty$ (and hence non-complete and metrizable). It has been also shown that the Pontryagin duality between the spaces $D(R)$ and $D'(R)$ can not be extended to their subspaces and quotients. In solving all of those problems a method of effective constructing, in locally convex spaces, some sequentially closed non-closed subsets of different types (countable, convex, vector subspaces etc.) has been derived. This method has also an independent interest and has been used to solve some other problems, for example to construct infinitely differentiable discontinuous functions on locally convex spaces (M. O. Smolyanova). Besides by this method it has been possible to solve, using some properties of spaces $D(R)$ and $D'(R)$, five of twelve problems posed in the famous paper of Dieudonne and L. Schwartz. By that time those problems have been already solved by Grothendieck who needed, without this method, to construct for that purpose some special locally convex spaces. It has been proved (together with A. V. Uglanov) that the Wiener measure does not have any Hilbert support; this statement refutes a conjecture of F. A. Berezin according to which the $\sigma$-additivity of the Wiener measure can be deduced from the Minlos–Sazonov theorem. It has been shown (together with E. T. Shavgulidze) that the Hamiltonian Feynman measure (on the set of paths in the phase space) can be considered as an analytical continuation of a Gaussian measure; this statement refutes another Berezin's conjecture. Some infinite dimensional pseudodifferential operators with $pq$- and $qp$-symbols have been defined and (together with A. Yu. Khrennikov) an algebra of such operators have been constructed; by this way one more Berezin's problem have been solved. A theory of smooth functions and (together with S. V. Fomin) a theory of smooth measures on infinite dimensional spaces have been developed. It has been shown (together with J. Kupsch) that there does not exist any Hilbert norm on a tensor algebra (including the Grassman algebra) that satisfies the estimate $\|xy\|\le c\|x\|\|y\|$ with the constant $c=1$ but such a norm has been constructed for $c=\sqrt{3}$; this means that a problem tracing back to B. deWitt is solved. Some representations of solutions for stochastic Schroedinger–Belavkin equations by Feynman path integrals are obtained (together with S. Albeverio, V. M. Kolokol'tsov, A. Truman). It is proved (together with M. O. Smolyanova) a Prigogine's conjecture about irreducibility of Liouvillian dynamics to Hamiltonian dynamics. Some connections between Levy Laplacians and (quantum) stochastic processes are described (together with L. Accardi). Surface measures on trajectories in Riemannian submanifolds of Euclidian spaces (and Riemannian manifolds) generated by measures on trajectories in enveloping spaces are introduced and (together with H. v. Weizsaecker) their properties are investigated. In particular it is shown that in the case of the Wiener measure on trajectories in the enveloping manifold the corresponding surface measure is equivalent to the Wiener measure on trajectories in the submanifolds and the corresponding density is calculated. Some Feynman and Feynman–Kac formulas for solutions of Schroedinger equations on Riemannian manifolds (including stochastic equations) are obtained (together with A. Truman); by this way some problems tracing back to C. deWitt-Morett and D. Elworthy are solved.


A scientific biography and some additional information can be found in the paper published in the Moscow State University Mathematical Bulletin, 1998, no. 5 (in Russian).

Main publications:
  • Kupsch J., Smolyanov O. G. Functional representations for Fock superalgebras // Infinite Dimensional Analysis, Quantum Probability and Related Topics, v. 1, no. 2, 1998, 285–324.
  • Smolyanov O. G., Weizsaecker H. v., Wittich O. Brownian motion on a manifiold as limit of stepwise conditioned standard Brownian motions // Canadian Mathematical Society Conference Proceedings, v. 29, 2000, 589–602.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. John E. Gough, Tudor S. Ratiu, Oleg G. Smolyanov, “Quantum Anomalies via Differential Properties of Lebesgue–Feynman Generalized Measures”, Tr. Mat. Inst. Steklova, 310 (2020),  107–118  mathnet; Proc. Steklov Inst. Math., 310 (2020), 98–107
2. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Randomizes hamiltonian mechanics”, Dokl. Akad. Nauk, 486:6 (2019),  635–658  mathnet  elib
3. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman Formulas and the Law of Large Numbers for Random One-Parameter Semigroups”, Tr. Mat. Inst. Steklova, 306 (2019),  210–226  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 306 (2019), 196–211  isi  scopus
4. V. V. Kozlov, O. G. Smolyanov, “Hamiltonian approach to secondary quantization”, Dokl. Akad. Nauk, 483:2 (2018),  138–142  mathnet  elib; Dokl. Math., 98:3 (2018), 571–574  isi  scopus
5. V. V. Kozlov, O. G. Smolyanov, “Two Theorems on Isomorphisms of Measure Spaces”, Mat. Zametki, 104:5 (2018),  781–784  mathnet  mathscinet  elib; Math. Notes, 104:5 (2018), 758–761  isi  scopus
6. V. Zh. Sakbaev, O. G. Smolyanov, “Feynman calculus for random operator-valued functions and their applications”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160:2 (2018),  373–383  mathnet  isi
7. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. RAN. Ser. Mat., 80:6 (2016),  141–172  mathnet  mathscinet  elib; Izv. Math., 80:6 (2016), 1131–1158  isi  scopus
8. V. V. Kozlov, O. G. Smolyanov, “Invariant and quasi-invariant measures on infinite-dimensional spaces”, Dokl. Akad. Nauk, 465:5 (2015),  527–531  mathnet  elib; Dokl. Math., 92:3 (2015), 743–746  isi  scopus
9. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman formulas as a method of averaging random Hamiltonians”, Tr. Mat. Inst. Steklova, 285 (2014),  232–243  mathnet  elib; Proc. Steklov Inst. Math., 285 (2014), 222–232  isi  elib  scopus
10. V. V. Kozlov, O. G. Smolyanov, “Hamiltonian aspects of quantum theory”, Dokl. Akad. Nauk, 444:6 (2012),  607–611  mathnet  mathscinet  zmath; Dokl. Math., 85:3 (2012), 416–420  isi  scopus
11. G. G. Amosov, V. Zh. Sakbaev, O. G. Smolyanov, “Linear and nonlinear liftings of states of quantum systems”, Russ. J. Math. Phys., 19:4 (2012),  417–427  mathnet  mathscinet  zmath  isi  scopus
12. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian”, TMF, 172:1 (2012),  122–137  mathnet  mathscinet  elib; Theoret. and Math. Phys., 172:1 (2012), 987–1000  isi  elib  scopus
13. V. V. Kozlov, O. G. Smolyanov, “The relativistic Poincaréм model”, Dokl. Akad. Nauk, 428:2 (2009),  171–176  mathnet  mathscinet; Dokl. Math., 80:2 (2009), 769–774  isi  scopus
14. J. Kupsch, O. G. Smolyanov, “Generalized Wiener-Segal-Fock representations and Feynman formulae”, Dokl. Akad. Nauk, 425:1 (2009),  15–19  mathnet  mathscinet; Dokl. Math., 79:2 (2009), 153–157  isi  scopus
15. L. Accardi, O. G. Smolyanov, “Generalized Lévy Laplacians and Cesàro means”, Dokl. Akad. Nauk, 424:5 (2009),  583–587  mathnet  mathscinet  elib; Dokl. Math., 79:1 (2009), 90–93  isi  scopus
16. O. G. Smolyanov, N. N. Shamarov, “Feynman Formulas and Path Integrals for Evolution Equations with the Vladimirov Operator”, Tr. Mat. Inst. Steklova, 265 (2009),  229–240  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 265 (2009), 217–228  isi  elib  scopus
17. O. G. Smolyanov, N. N. Shamarov, “Representation of solutions to a heat conduction equation with Vladimirov’s operator by functional integrals”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, 4,  16–22  mathnet  mathscinet  zmath
18. V. V. Kozlov, O. G. Smolyanov, “Weak convergence of states in quantum statistical mechanics”, Dokl. Akad. Nauk, 417:2 (2007),  180–184  mathnet  mathscinet; Dokl. Math., 76:3 (2007), 958–961  isi  scopus
19. V. V. Kozlov, O. G. Smolyanov, “Information entropy in problems of classical and quantum statistical mechanics”, Dokl. Akad. Nauk, 411:5 (2006),  587–590  mathnet  mathscinet; Dokl. Math., 74:3 (2006), 910–913  isi  scopus
20. J. Kupsch, O. G. Smolyanov, “Exact master equations describing reduced dynamics of the Wigner function”, Fundam. Prikl. Mat., 12:5 (2006),  203–219  mathnet  mathscinet  zmath; J. Math. Sci., 150:6 (2008), 2598–2608  scopus
21. V. V. Kozlov, O. G. Smolyanov, “Wigner function and diffusion in collisionfree media of quantum particles”, Teor. Veroyatnost. i Primenen., 51:1 (2006),  109–125  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 51:1 (2007), 168–181  isi  scopus
22. J. E. Gough, O. O. Obrezkov, O. G. Smolyanov, “Randomized Hamiltonian Feynman integrals and Shrödinger–Itô stochastic equations”, Izv. RAN. Ser. Mat., 69:6 (2005),  3–20  mathnet  mathscinet  zmath  elib; Izv. Math., 69:6 (2005), 1081–1098  isi  elib  scopus
23. O. G. Smolyanov, S. A. Shkarin, “Gateaux complex differentiability and continuity”, Izv. RAN. Ser. Mat., 68:6 (2004),  157–168  mathnet  mathscinet  zmath; Izv. Math., 68:6 (2004), 1217–1227  isi  scopus
24. O. G. Smolyanov, J. Kupsch, “Asymptotic Decoherence in Infinite-Dimensional Quantum Systems with Quadratic Hamiltonians”, Mat. Zametki, 73:1 (2003),  143–148  mathnet  mathscinet  zmath; Math. Notes, 73:1 (2003), 136–141  isi
25. L. Accardi, O. G. Smolyanov, “Lévy–Laplace Operators in Functional Rigged Hilbert Spaces”, Mat. Zametki, 72:1 (2002),  145–150  mathnet  mathscinet  zmath; Math. Notes, 72:1 (2002), 129–134  isi  scopus
26. O. G. Smolyanov, S. A. Shkarin, “Structure of spectra of linear operators in Banach spaces”, Mat. Sb., 192:4 (2001),  99–114  mathnet  mathscinet  zmath; Sb. Math., 192:4 (2001), 577–591  isi  scopus
27. O. G. Smolyanov, A. Trumen, “Feynman Formulas for Solutions of the Schrödinger Equation on Compact Riemannian Manifolds”, Mat. Zametki, 68:5 (2000),  789–793  mathnet  mathscinet  zmath; Math. Notes, 68:5 (2000), 668–671  isi
28. O. G. Smolyanov, J. Kupsch, “Bogolyubov transformations in Wiener–Segal–Fock space”, Mat. Zametki, 68:3 (2000),  474–479  mathnet  mathscinet  zmath; Math. Notes, 68:3 (2000), 409–414  isi
29. O. G. Smolyanov, A. Trumen, “Schrödinger–Belavkin equations and associated Kolmogorov and Lindblad equations”, TMF, 120:2 (1999),  193–207  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 120:2 (1999), 973–984  isi
30. O. G. Smolyanov, A. Trumen, “Change of variable formulas for Feynman pseudomeasures”, TMF, 119:3 (1999),  355–367  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 119:3 (1999), 677–686  isi
31. O. G. Smolyanov, L. Accardi, “Extensions of spaces with cylindrical measures and supports of measures determined by the Lévy Laplacian”, Mat. Zametki, 64:4 (1998),  483–492  mathnet  mathscinet  zmath  elib; Math. Notes, 64:4 (1998), 421–428  isi
32. O. G. Smolyanov, “Stochastic Schrödinger–Belavkin equation and the corresponding equations of Kolmogorov and Lindblad”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, 4,  19–24  mathnet  mathscinet  zmath
33. N. V. Norin, O. G. Smolyanov, “Logarithmic derivatives of measures, and Gibbs distributions”, Dokl. Akad. Nauk, 354:4 (1997),  456–460  mathnet  mathscinet  zmath
34. S. A. Albeverio, O. G. Smolyanov, “Infinite-dimensional stochastic Schrödinger–Belavkin equations”, Uspekhi Mat. Nauk, 52:4(316) (1997),  197–198  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:4 (1997), 822–823  isi  scopus
35. O. G. Smolyanov, “Differentiable measures on current groups”, Tr. Mat. Inst. Steklova, 217 (1997),  182–188  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 217 (1997), 174–180
36. L. Accardi, O. G. Smolyanov, “Transformations of Gaussian measures generated by the Lévy–Laplacian, and generalized traces”, Dokl. Akad. Nauk, 350:1 (1996),  5–8  mathnet  mathscinet  zmath
37. J. Kupsch, O. G. Smolyanov, “Models of the symmetric Fock algebra”, Mat. Zametki, 60:6 (1996),  939–942  mathnet  mathscinet  zmath; Math. Notes, 60:6 (1996), 710–713  isi
38. L. Accardi, O. G. Smolyanov, M. O. Smolyanova, “Change of variable formulas for infinite-dimensional distributions”, Mat. Zametki, 60:2 (1996),  288–292  mathnet  mathscinet  zmath; Math. Notes, 60:2 (1996), 212–215  isi
39. H. von Weizsäcker, O. G. Smolyanov, “Formulae with logarithmic derivatives of measures related to the quantization of infinite-dimensional Hamiltonian systems”, Uspekhi Mat. Nauk, 51:2(308) (1996),  149–150  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:2 (1996), 357–358  isi  scopus
40. O. G. Smolyanov, “Smooth measures on loop groups”, Dokl. Akad. Nauk, 345:4 (1995),  455–458  mathnet  mathscinet  zmath
41. L. Accardi, O. G. Smolyanov, “A Gaussian process generated by the Lévy Laplacian, and the corresponding Feynman–Kac formula”, Dokl. Akad. Nauk, 342:4 (1995),  442–445  mathnet  mathscinet  zmath
42. Kh. von Weizsäcker, O. G. Smolyanov, “Smooth curves in spaces of measures, and shifts of differentiable measures along vector fields”, Dokl. Akad. Nauk, 339:5 (1994),  584–587  mathnet  mathscinet  zmath; Dokl. Math., 50:3 (1995), 476–481
43. O. G. Smolyanov, M. O. Smolyanova, “The Feynman integral and nonlinear transformations of a phase space”, Dokl. Akad. Nauk, 336:1 (1994),  29–32  mathnet  mathscinet  zmath; Dokl. Math., 49:3 (1994), 465–470
44. S. G. Lobanov, O. G. Smolyanov, “Ordinary differential equations in locally convex spaces”, Uspekhi Mat. Nauk, 49:3(297) (1994),  93–168  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:3 (1994), 97–175  isi
45. O. G. Smolyanov, M. O. Smolyanova, “Transformations of Feynman integral under some nonlinear transformations of the phase space”, TMF, 100:1 (1994),  3–13  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 100:1 (1994), 803–810  isi
46. O. G. Smolyanov, “The Holmgren theorem for stochastic differential equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1994, 1,  54–59  mathnet  mathscinet  zmath
47. N. V. Norin, O. G. Smolyanov, “Some results on logarithmic derivatives of measures on a locally convex space”, Mat. Zametki, 54:6 (1993),  135–138  mathnet  mathscinet  zmath; Math. Notes, 54:6 (1993), 1277–1279  isi
48. L. Accardi, P. Rozelli, O. G. Smolyanov, “Brownian motion generated by the Levy Laplacian”, Mat. Zametki, 54:5 (1993),  144–148  mathnet  mathscinet  zmath; Math. Notes, 54:5 (1993), 1174–1177  isi
49. 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  mathnet  mathscinet  zmath; Dokl. Math., 45:2 (1992), 492–496
50. O. G. Smolyanov, M. O. Smolyanova, “Shifts of Feynman measure along vector fields”, Mat. Zametki, 52:3 (1992),  154–156  mathnet  mathscinet  zmath; Math. Notes, 52:3 (1992), 990–992  isi
51. 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
52. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Uspekhi Mat. Nauk, 45:3(273) (1990),  3–83  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:3 (1990), 1–104  isi
53. 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  mathnet  mathscinet  zmath; Dokl. Math., 40:3 (1990), 552–557
54. O. G. Smolyanov, E. T. Shavgulidze, “The Fourier transform and pseudodifferential operators in superanalysis”, Dokl. Akad. Nauk SSSR, 299:4 (1988),  816–820  mathnet  mathscinet  zmath; Dokl. Math., 37:2 (1988), 476–481
55. O. G. Smolyanov, A. Yu. Khrennikov, “Algebra of infinite-dimensional pseudodifferential operators”, Dokl. Akad. Nauk SSSR, 292:6 (1987),  1310–1314  mathnet  mathscinet  zmath
56. O. G. Smolyanov, “de Rham currents and the Stokes formula in Hilbert space”, Dokl. Akad. Nauk SSSR, 286:3 (1986),  554–558  mathnet  mathscinet  zmath
57. O. G. Smolyanov, A. Yu. Khrennikov, “The central limit theorem for generalized measures on infinite-dimensional spaces”, Dokl. Akad. Nauk SSSR, 281:2 (1985),  279–283  mathnet  mathscinet  zmath
58. Yu. L. Daleckiĭ, O. G. Smoljanov, “On the weak sequential completeness of the spaces of Radon measures”, Teor. Veroyatnost. i Primenen., 29:1 (1984),  141–147  mathnet  mathscinet  zmath; Theory Probab. Appl., 29:1 (1985), 142–147  isi
59. O. G. Smolyanov, “Topology of the spaces $D$ and $D'$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1984, 1,  66–68  mathnet  mathscinet  zmath
60. O. G. Smolyanov, “The Gross–Sazonov theorem for sign-variable cylindrical measures”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1983, 4,  4–12  mathnet  mathscinet  zmath
61. O. G. Smolyanov, “Infinite-dimensional pseudodifferential operators and Schrödinger quantization”, Dokl. Akad. Nauk SSSR, 263:3 (1982),  558–562  mathnet  mathscinet  zmath
62. O. G. Smolyanov, “A method of proof of the uniqueness theorem for evolutionary differential equations”, Mat. Zametki, 25:2 (1979),  259–269  mathnet  mathscinet  zmath; Math. Notes, 25:2 (1979), 135–140  isi
63. O. G. Smolyanov, “Higher derivatives of mappings of locally convex spaces”, Mat. Zametki, 22:5 (1977),  729–744  mathnet  mathscinet  zmath; Math. Notes, 22:5 (1977), 899–906
64. O. G. Smolyanov, S. V. Fomin, “Measures on linear topological spaces”, Uspekhi Mat. Nauk, 31:4(190) (1976),  3–56  mathnet  mathscinet  zmath; Russian Math. Surveys, 31:4 (1976), 1–53
65. O. G. Smolyanov, “Linear representations of evolution differential equations”, Dokl. Akad. Nauk SSSR, 221:6 (1975),  1288–1291  mathnet  mathscinet  zmath
66. O. G. Smolyanov, “Almost closed subsets of countable products of locally convex spaces”, Tr. Mosk. Mat. Obs., 32 (1975),  61–76  mathnet  mathscinet  zmath
67. O. G. Smolyanov, “The class of spaces in which the theorem on the bounded differentiability of the inverse mapping is valid”, Mat. Zametki, 17:5 (1975),  703–709  mathnet  mathscinet  zmath; Math. Notes, 17:5 (1975), 418–421
68. O. G. Smolyanov, “The size of the classes of hypercomplete spaces and spaces that satisfy the Kreĭn–Šmul'jan condition”, Uspekhi Mat. Nauk, 30:1(181) (1975),  259–260  mathnet  mathscinet  zmath
69. O. G. Smolyanov, “Certain complete spaces of smooth mappings of pseudotopological linear spaces”, Uspekhi Mat. Nauk, 29:4(178) (1974),  181–182  mathnet  mathscinet  zmath
70. O. G. Smolyanov, “Sequentially closed subsets of products of locally convex spaces”, Funktsional. Anal. i Prilozhen., 7:1 (1973),  88–89  mathnet  mathscinet  zmath; Funct. Anal. Appl., 7:1 (1973), 80–81
71. O. G. Smolyanov, A. V. Uglanov, “Every Hilbert subspace of a Wiener space has measure zero”, Mat. Zametki, 14:3 (1973),  369–374  mathnet  mathscinet  zmath; Math. Notes, 14:3 (1973), 772–774
72. O. G. Smolyanov, “Linear differential operators in spaces of measures and functions on Hilbert space”, Uspekhi Mat. Nauk, 28:5(173) (1973),  251–252  mathnet  mathscinet  zmath
73. V. I. Averbukh, O. G. Smolyanov, S. V. Fomin, “Generalized functions and differential equations in linear spaces. II. Differential operators and their Fourier transforms”, Tr. Mosk. Mat. Obs., 27 (1972),  249–262  mathnet  mathscinet  zmath
74. O. G. Smolyanov, “Several results on fully complete spaces and hereditarily complete spaces”, Uspekhi Mat. Nauk, 27:2(164) (1972),  181–182  mathnet  mathscinet  zmath
75. O. G. Smolyanov, “The space $D$ is not hereditarily complete”, Izv. Akad. Nauk SSSR Ser. Mat., 35:3 (1971),  682–696  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:3 (1971), 696–710
76. V. I. Averbukh, O. G. Smolyanov, S. V. Fomin, “Generalized functions and differential equations in linear spaces. I. Differentiable measures”, Tr. Mosk. Mat. Obs., 24 (1971),  133–174  mathnet  mathscinet  zmath
77. O. G. Smolyanov, “Measurable linear manifolds in products of linear spaces with measure”, Mat. Zametki, 5:5 (1969),  623–634  mathnet  mathscinet  zmath; Math. Notes, 5:5 (1969), 374–379
78. O. G. Smolyanov, “Almost closed linear subspaces of strict inductive limits of sequences of Fréchet spaces”, Mat. Sb. (N.S.), 80(122):4(12) (1969),  513–520  mathnet  mathscinet  zmath; Math. USSR-Sb., 9:4 (1969), 479–485
79. V. I. Averbukh, O. G. Smolyanov, “The various definitions of the derivative in linear topological spaces”, Uspekhi Mat. Nauk, 23:4(142) (1968),  67–116  mathnet  mathscinet  zmath; Russian Math. Surveys, 23:4 (1968), 67–113
80. V. I. Averbukh, O. G. Smolyanov, “Differentiation in linear topological spaces”, Dokl. Akad. Nauk SSSR, 173:4 (1967),  735–738  mathnet  mathscinet  zmath
81. V. I. Averbukh, O. G. Smolyanov, “The theory of differentiation in linear topological spaces”, Uspekhi Mat. Nauk, 22:6(138) (1967),  201–260  mathnet  mathscinet  zmath; Russian Math. Surveys, 22:6 (1967), 201–258
82. O. G. Smolyanov, “Measurable polylinear and power functionals in certain linear spaces with measure”, Dokl. Akad. Nauk SSSR, 170:3 (1966),  526–529  mathnet  mathscinet  zmath
83. O. G. Smolyanov, “Isomorphism of some functional measure spaces”, Uspekhi Mat. Nauk, 21:3(129) (1966),  231–232  mathnet
84. O. G. Smolyanov, “On linear topological spaces not satisfying the first axiom of countability”, Uspekhi Mat. Nauk, 19:6(120) (1964),  199–200  mathnet  mathscinet  zmath

85. P. S. Aleksandrov, I. M. Gel'fand, A. N. Kolmogorov, E. V. Maikov, V. P. Maslov, O. A. Oleinik, Ya. G. Sinai, O. G. Smolyanov, V. M. Tikhomirov, “In memory of Sergei Vasil'evich Fomin”, Uspekhi Mat. Nauk, 31:4(190) (1976),  199–212  mathnet  mathscinet  zmath; Russian Math. Surveys, 31:4 (1976), 105–220
86. V. I. Averbukh, O. G. Smolyanov, “An addendum to the article: “Different definitions of derivative in linear topological spaces””, Uspekhi Mat. Nauk, 23:5(143) (1968),  223–224  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Quantum anomalies and differential properties of generalized Lebesgue-Feynman measures
Oleg Smolyanov
International Conference on Mathematical Physics in Memory of Academic V. S. Vladimirov
November 23, 2020 18:30
2. Функциональные интегралы и регуляризованные следы в суперанализе
O. G. Smolyanov, E. T. Shavgulidze
Infinite dimensional analysis and mathematical physics
October 26, 2020 18:30
3. Квантование по Шрёдингеру бесконечномерных гамильтоновых систем с неквадратичной функцией Гамильтона
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
October 19, 2020 18:30
4. Использование дифференциальных свойств обобщённых мер Лебега-Фейнмана при исследовании квантовых аномалий
J. E. Gough, T. S. Ratiu, O. G. Smolyanov
Infinite dimensional analysis and mathematical physics
October 12, 2020 18:30
5. Квантование по Шрёдингеру бесконечномерных гамильтоновых систем с неквадратичной функцией Гамильтона
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
September 7, 2020 18:30
6. Аналог унитарного преобразования Фурье в пространстве функций бесконечномерного аргумента
O. G. Smolyanov, N. N. Shamarov
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
April 16, 2020 11:00
7. Гамильтоново вторичное квантование
O. G. Smolyanov, N. N. Shamarov
Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov
September 13, 2019 18:30
8. Вторичное квантование по Вейлю бесконечномерных гамильтоновых систем
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
April 22, 2019 18:30
9. Derivatives of generalized measures and quantum anomalies
O. G. Smolyanov
Internaional conference «Modern Mathematical Physics. Vladimirov-95»
November 14, 2018 15:00   
10. Постановки задач
O. G. Smolyanov
Infinite dimensional analysis and mathematical physics
September 10, 2018 18:30
11. Функциональные интегралы Фейнмана и квантовые аномалии
O. G. Smolyanov
Seminar on Theory of Functions of Real Variables
April 20, 2018 18:30
12. Совместное заседание Московского математического общества и кафедры теории функций и функционального анализа механико-математического МГУ, посвященное 100-летию Георгия Евгеньевича Шилова
V. I. Bogachev, O. G. Smolyanov, V. M. Tikhomirov
Meetings of the Moscow Mathematical Society
November 7, 2017
13. Цилиндрические меры, вероятностные распределения и статистическая физика
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
April 17, 2017 18:30
14. Quantum anomalies and transformations of Feynman path integrals
Oleg Smolyanov
New Trends in Mathematical and Theoretical Physics
October 4, 2016 16:00   
15. О квантовой запутанности
O. G. Smolyanov
Infinite dimensional analysis and mathematical physics
October 26, 2015 18:40
16. О преобразованиях Фурье с коммутирующими и антикоммутирующими переменными
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
October 19, 2015 18:30
17. Коммутационные соотношения для псевдо-дифференциальных операторов в пространстве антикоммутирующих переменных
O. G. Smolyanov, N. N. Shamarov
Infinite dimensional analysis and mathematical physics
September 14, 2015 18:30
18. Differential operators and Feynman formulas
O. G. Smolyanov
Differential geometry and applications
November 10, 2014 16:45
19. Формулы Фейнмана, проблема Гельфанда и близкие вещи
O. G. Smolyanov
I. M. Gelfand and Modern Mathematics
December 19, 2013 10:00   
20. Формулы Фейнмана и Фейнмана-Каца и их применения
O. G. Smolyanov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 27, 2013 18:30
21. Формулы Фейнмана–Каца и Фейнмана для групп и полугрупп Шредингера
O. G. Smolyanov
Conference "Mathematical Physics. Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov
November 14, 2013 11:30   
22. Hamilton, Feynman and Wigner structures in the theory of open quantum systems
O. G. Smolyanov
International conference "QP 34 – Quantum Probability and Related Topics"
September 20, 2013 14:30   
23. 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
24. Measures on infinite-dimensional spaces and the Bogolyubov equations
O. G. Smolyanov
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 9, 2011 12:00
25. Дифференцируемые меры на бесконечномерных пространствах
O. G. Smolyanov
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
February 28, 2008 11:00
26. Представление решений эволюционных уравнений с оператором Владимирова с помощью интегралов по траекториям в $Q_p$
O. G. Smolyanov, N. N. Shamarov
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 25, 2007 11:00
27. Feynman formulae and path integrals
O. G. Smolyanov
Steklov Mathematical Institute Seminar
February 15, 2007 16:00   
28. Операторы Лапласа–Леви
O. G. Smolyanov
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
April 6, 2006
29. Интегрирование по траекториям в римановых многообразиях
O. G. Smolyanov
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 21, 2004

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