Edit Profile (opens in new tab) Smolyanov, Oleg Georgievich Compute Distance To: Compute Author ID: smolyanov.oleg-georgievich Published as: Smolyanov, O. G.; Smolyanov, Oleg G.; Smolyanov, Oleg; Smolyanov, O.; Smol’yanov, O. G.; Smolianov, O. G. Further Spellings: Смолянов Олег Георгиевич External Links: MGP · Math-Net.Ru Documents Indexed: 251 Publications since 1964, including 3 Books 1 Contribution as Editor Biographic References: 2 Publications Co-Authors: 75 Co-Authors with 214 Joint Publications 2,901 Co-Co-Authors all top 5 Co-Authors 36 single-authored 27 von Weizsäcker, Heinrich 15 Sakbaev, Vsevolod Zhanovich 15 Shavgulidze, Eugene T. 14 Averbukh, Vladimir I. 14 Kozlov, Valeriĭ Vasil’evich 14 Wittich, Olaf 13 Accardi, Luigi 13 Khrennikov, Andreĭ Yur’evich 12 Albeverio, Sergio A. 12 Gough, John E. 12 Kupsch, Joachim 11 Ratiu, Tudor Stefan 11 Truman, Aubrey 10 Shamarov, Nikolaĭ Nikolaevich 7 Kinderknecht, Yana A. 7 Orlov, Yurii N. 7 Sidorova, Nadia 6 Smolyanova, M. O. 5 Bogachev, Vladimir Igorevich 5 Fomin, Sergeĭ Vasil’evich 4 Kupsch, I. 4 Montaldi, James A. 4 Schilling, René Leander 4 Shkarin, Stanislav A. 3 Belavkin, Viacheslav 3 Grothaus, Martin 3 Obrezkov, Oleg O. 3 Sadovnichiĭ, Viktor Antonovich 2 Aleksandrov, Pavel Sergeevich 2 Dalets’kyĭ, Yuriĭ L’vovych 2 García-Naranjo, Luis C. 2 Gel’fand, Israil’ Moiseevich 2 Kolmogorov, Andreĭ Nikolaevich 2 Kolokoltsov, Vassili N. 2 Léandre, Rémi 2 Maikov, E. V. 2 Maslov, Viktor Pavlovich 2 Norin, N. V. 2 Oleĭnik, Ol’ga Arsen’evna 2 Sakbaev, V. G. 2 Shelkovich, Vladimir M. 2 Sinaĭ, Yakov Grigor’evich 2 Tikhomirov, Vladimir Mikhaĭlovich 2 Tolstyga, D. S. 1 Amosov, Grigoriĭ Gennad’evich 1 Antoniou, Ioannis E. 1 Antoniou, Ya. 1 Belyaev, Alekseĭ Aleksandrovich 1 Borodin, Petr A. 1 Böttcher, Björn 1 Davies, Ian M. 1 Durran, Richard M. 1 Gadella, Manuel 1 Ibragimov, Il’dar Abdullovich 1 Kashin, Boris Sergeevich 1 Kolesnikov, Alexander V. 1 Konyagin, Sergeĭ Vladimirovich 1 Kosov, Egor D. 1 Kpekpassi, M. 1 Kravtseva, A. K. 1 Lobanov, S. G. 1 Neate, Andrew D. 1 Querdiane, Habib 1 Rozelli, P. 1 Schachermayer, Walter 1 Shaposhnikov, Alexander V. 1 Shaposhnikov, Stanislav V. 1 Shiryaev, Al’bert Nikolaevich 1 Shkalikov, Andreĭ Andreevich 1 Tokarev, A. G. 1 Tolmachev, N. A. 1 Treshchev, Dmitriĭ Valer’evich 1 Trumen, A. 1 Uglanov, Alexey V. 1 Zamana, Konstantin Yur’evich all top 5 Serials 101 Doklady Mathematics 16 Mathematical Notes 13 Russian Journal of Mathematical Physics 9 Russian Mathematical Surveys 9 Uspekhi Matematicheskikh Nauk [N. S.] 9 Soviet Mathematics. Doklady 7 Moscow University Mathematics Bulletin 6 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 6 Doklady Akademii Nauk 5 Infinite Dimensional Analysis, Quantum Probability and Related Topics 5 Proceedings of the Steklov Institute of Mathematics 4 Journal of Mathematical Physics 4 Theoretical and Mathematical Physics 3 International Journal of Theoretical Physics 3 Teoriya Veroyatnosteĭ i eë Primeneniya 3 Transactions of the Moscow Mathematical Society 3 Trudy Moskovskogo Matematicheskogo Obshchestva 3 Russian Academy of Sciences. Doklady. Mathematics 3 Izvestiya: Mathematics 2 Theory of Probability and its Applications 2 Journal of Functional Analysis 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Potential Analysis 1 Matematicheskie Zametki 1 Reviews in Mathematical Physics 1 Conferenze del Seminario di Matematica dell’Università di Bari 1 Functional Analysis and its Applications 1 Matematicheskiĭ Sbornik. Novaya Seriya 1 Mathematics of the USSR. Izvestiya 1 Proceedings of the American Mathematical Society 1 Note di Matematica 1 Computational Mathematics and Mathematical Physics 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Open Systems & Information Dynamics 1 Springer Monographs in Mathematics 1 Moscow Lectures all top 5 Fields 112 Quantum theory (81-XX) 83 Functional analysis (46-XX) 53 Probability theory and stochastic processes (60-XX) 52 Operator theory (47-XX) 42 Global analysis, analysis on manifolds (58-XX) 37 Partial differential equations (35-XX) 33 Measure and integration (28-XX) 16 Statistical mechanics, structure of matter (82-XX) 11 Ordinary differential equations (34-XX) 11 Mechanics of particles and systems (70-XX) 8 Dynamical systems and ergodic theory (37-XX) 5 Differential geometry (53-XX) 4 History and biography (01-XX) 4 Relativity and gravitational theory (83-XX) 4 Systems theory; control (93-XX) 3 General topology (54-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 177 Publications have been cited 1,096 times in 504 Documents Cited by ▼ Year ▼ Hamiltonian Feynman path integrals via the Chernoff formula. Zbl 1060.58009Smolyanov, O. G.; Tokarev, A. G.; Truman, A. 71 2002 The various definitions of the derivative in linear topological spaces. Zbl 0196.15702Averbukh, V. I.; Smolyanov, O. G. 56 1968 The theory of differentiation in linear topological spaces. Zbl 0312.46054Averbukh, V. I.; Smolyanov, O. G. 51 1967 Chernoff’s theorem and discrete time approximations of Brownian motion on manifolds. Zbl 1107.58014Smolyanov, Oleg G.; von Weizsäcker, Heinrich; Wittich, Olaf 43 2007 Generalized functions and differential equations in linear spaces. I: Differentiable measures. Zbl 0234.28005Averbukh, V. I.; Smolyanov, O. G.; Fomin, S. V. 32 1971 Measures on linear topological spaces. Zbl 0364.28010Smolyanov, O. G.; Fomin, S. V. 31 1976 Feynman formulas as a method of averaging random Hamiltonians. Zbl 1304.81082Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 27 2014 Unbounded random operators and Feynman formulae. Zbl 1422.47049Orlov, Yurii N.; Sakbaev, Vsevolod Zh.; Smolyanov, Oleg G. 26 2016 Topological vector spaces and their applications. Translated from the Russian. Expanded and revised translation, originally published 2012. Zbl 1378.46001Bogachev, V. I.; Smolyanov, O. G. 25 2017 Brownian motion on a manifold as limit of stepwise conditioned standard Brownian motions. Zbl 0978.58015Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 22 2000 Analytic properties of infinite-dimensional distributions. Zbl 0708.60049Bogachëv, V. I.; Smolyanov, O. G. 22 1990 Feynman formulas for particles with position-dependent mass. Zbl 1159.35426Gadella, M.; Smolyanov, O. G. 17 2008 Smooth probability measures and associated differential operators. Zbl 0936.60052Smolyanov, O. G.; von Weizsäcker, H. 17 1999 Die Theorie der Differentiation in linearen topologischen Räumen. Zbl 0195.42601Averbukh, V. I.; Smolyanov, O. G. 16 1967 On Laplacians and traces. Zbl 1041.46516Accardi, L.; Smolianov, O. G. 14 1993 Lagrangian Feynman formulas for second-order parabolic equations in bounded and unbounded domains. Zbl 1204.47096Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G. 14 2010 Differentiable families of measures. Zbl 0795.46015Smolyanov, O. G.; von Weizsäcker, H. 14 1993 Surface measures and initial boundary value problems generated by diffusions with drift. Zbl 1156.58014Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 13 2007 Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G. 13 2012 The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold. Zbl 1046.58014Sidorova, Nadezda A.; Smolyanov, Oleg G.; von Weizsäcker, Heinrich; Wittich, Olaf 11 2004 Feynman formulae for Feller semigroups. Zbl 1213.47047Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L. 11 2010 Real and functional analysis. Zbl 1466.26002Bogachev, Vladimir I.; Smolyanov, Oleg G. 11 2020 Representation of solutions of linear evolution superdifferential equations of second order by functional integrals. Zbl 0706.35119Smolyanov, O. G.; Shavgulidze, E. T. 11 1990 Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions. Zbl 1335.81103Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G. 9 2016 Functional representations for Fock superalgebras. Zbl 0913.46059Kupsch, Joachim; Smolyanov, Oleg G. 9 1998 Infinite-dimensional Schrödinger equations with polynomial potentials and Feynman path integrals. Zbl 1327.81257Smolyanov, O. G.; Shavgulidze, E. T. 9 2006 Diffusion on compact Riemannian manifolds, and surface measures. Zbl 1047.58006von Weizsäcker, H.; Smolyanov, O. G.; Wittich, O. 9 2000 Infinite-dimensional pseudodifferential operators and Schrödinger quantization. Zbl 0534.35087Smolyanov, O. G. 9 1982 Generalized Lévy Laplacians and Cesàro means. Zbl 1261.46034Accardi, L.; Smolyanov, O. G. 9 2009 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143Ratiu, T. S.; Smolyanov, O. G. 9 2013 Ordinary differential equations in locally convex spaces. Zbl 0834.34076Lobanov, S. G.; Smolyanov, O. G. 9 1994 Verallgemeinerte Funktionen und Differentialgleichungen in linearen Räumen. Zbl 0247.46055Averbukh, V. I.; Smolyanov, O. G.; Fomin, S. V. 9 1972 Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator. Zbl 1185.35351Smolyanov, O. G.; Shamarov, N. N. 8 2008 Schrödinger-Belavkin equations and associated Kolmogorov and Lindblad equations. Zbl 1113.81310Smolyanov, O. G.; Truman, A. 8 1999 Feynman formula for a class of second-order parabolic equations in a bounded domain. Zbl 1218.81037Butko, Ya. A.; Grothaus, M.; Smolyanov, O. G. 8 2008 Feynman formulas and path integrals for evolution equations with the Vladimirov operator. Zbl 1180.81069Smolyanov, O. G.; Shamarov, N. N. 8 2009 Feynman formulae for evolutionary equations. Zbl 1173.58006Smolyanov, Oleg G. 8 2009 Feynman formulas for evolution equations with Lévy Laplacians on infinite-dimensional manifolds. Zbl 1327.58033Accardi, L.; Smolyanov, O. G. 8 2006 Feynman-Kac and Feynman formulas for infinite-dimensional equations with Vladimirov operator. Zbl 1251.35181Smolyanov, O. G.; Shamarov, N. N.; Kpekpassi, M. 8 2011 Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian. Zbl 1280.81046Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 8 2012 Classical and nonclassical Levy Laplacians. Zbl 1155.35482Accardi, L.; Smolyanov, O. G. 7 2007 Chernoff’s theorem and the construction of semigroups. Zbl 1057.47044Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 7 2003 Feynman formulas and path integrals for some evolution semigroups related to \(\tau\)-quantization. Zbl 1311.58006Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G. 7 2011 Non-Gaussian Lagrangian Feynman-Kac formulas. Zbl 1304.81086Sakbaev, V. Z.; Smolyanov, O. G.; Shamarov, N. N. 7 2014 Measurable polylinear and power functionals in certain linear spaces with a measure. Zbl 0161.11304Smolyanov, O. G. 7 1966 Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems. Zbl 1295.81097Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 7 2014 The Fourier transform and pseudodifferential operators in superanalysis. Zbl 0699.47036Smolyanov, O. G.; Shavgulidze, E. T. 7 1988 Hamiltonian aspects of quantum theory. Zbl 1260.81092Kozlov, V. V.; Smolyanov, O. G. 7 2012 Randomized Hamiltonian Feynman integrals and Schrödinger-Itô stochastic equations. Zbl 1133.35109Gough, J.; Obrezkov, O. O.; Smolyanov, O. G. 7 2005 Continuous quantum measurement: Local and global approaches. Zbl 0894.47058Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G. 6 1997 Kolmogorov probability spaces describing accardi models of quantum correlations. Zbl 1082.81023Khrennikov, Andrei; Smolyanov, O. G.; Truman, A. 6 2005 States of quantum systems and their liftings. Zbl 1014.81009Kupsch, Joachim; Smolyanov, Oleg G.; Sidorova, Nadejda A. 6 2001 Wigner function and diffusion in a collision-free medium of quantum particles. Zbl 1120.82005Kozlov, V. V.; Smolyanov, O. G. 6 2007 Lévy Laplacian acting on operators. Zbl 1142.47362Accardi, L.; Querdiane, H.; Smolyanov, O. G. 6 2003 Dynamics of a quantum particle with discontinuous position-dependent mass. Zbl 1200.81054Sakbaev, V. G.; Smolyanov, O. G. 6 2010 Feynman formulas generated by self-adjoint extensions of the Laplacian. Zbl 1175.81106Smolyanov, O. G.; von Weizsäcker, H. 6 2009 Hamiltonian Feynman formulas for equations containing the vladimirov operator with variable coefficients. Zbl 1248.35242Smolyanov, O. G.; Shamarov, N. N. 6 2011 Change of variable formulas for infinite-dimensional distributions. Zbl 0898.46043Accardi, Luigi; Smolyanov, O. G.; Smolyanova, M. O. 6 1996 Feynman formulas for stochastic and quantum dynamics of particles in multidimensional domains. Zbl 1280.81049Smolyanov, O. G.; Tolstyga, D. S. 6 2013 Feynman formulas and the law of large numbers for random one-parameter semigroups. Zbl 1447.81026Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 5 2019 Hilbert norms for graded algebras. Zbl 0955.46026Kupsch, Joachim; Smolyanov, Oleg G. 5 2000 Schrodinger type semigroups via Feynman formulae and all that. Zbl 1354.47030Smolyanov, O. G. 5 2013 Transformations of measures via their generalized densities. Zbl 1322.46029Montaldi, J.; Smolyanov, O. G. 5 2014 Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G. 5 2011 Wigner measures on infinite-dimensional spaces and the Bogolyubov equations for quantum systems. Zbl 1236.81143Kozlov, V. V.; Smolyanov, O. G. 5 2011 Feynman description of the one-dimensional dynamics of particles whose masses piecewise continuously depend on coordinates. Zbl 1241.81077Smolyanov, Oleg G.; Tolstyga, D. S.; von Weizsäcker, Heinrich 5 2011 The space \(D\) is not hereditarily complete. Zbl 0249.46020Smolyanov, O. G. 5 1972 De Rham currents and Stokes’ formula in a Hilbert space. Zbl 0608.58004Smolyanov, O. G. 4 1986 The Feynman formulas for solving infinite-dimensional Schrödinger equations with polynomial potentials. Zbl 1247.81244Smolyanov, O. G.; Shavgulidze, Eugene T. 4 2003 Transformations of Feynman integrals under nonlinear transformations of the phase space. Zbl 1041.81549Smolyanov, O. G.; Smolyanova, M. O. 4 1994 Generalized functions and differential equations in linear spaces. I: Differentiable measures. Zbl 0295.28005Averbukh, V. I.; Smolyanov, O. G.; Fomin, S. V. 4 1974 Lévy–Laplace operators in functional rigged Hilbert spaces. Zbl 1033.35134Accardi, L.; Smolyanov, O. G. 4 2002 Every Hilbert subspace of a Wiener space has measure zero. Zbl 0369.28008Smolyanov, O. G.; Uglanov, A. V. 4 1973 Hamiltonian Feynman integrals for equations with the Vladimirov operator. Zbl 1210.46061Smolyanov, O. G.; Shamarov, N. N. 4 2010 Infinite-dimensional equation Liouville with respect to measures. Zbl 1210.37046Kozlov, V. V.; Smolyanov, O. G. 4 2010 Randomized Hamiltonian mechanics. Zbl 1428.81080Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 4 2019 Invariant and quasi-invariant measures on infinite-dimensional spaces. Zbl 1367.46037Kozlov, V. V.; Smolyanov, O. G. 4 2015 Quantum anomalies and logarithmic derivatives of Feynman pseudomeasures. Zbl 1341.81038Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 4 2015 The Gross-Sazonov theorem for signed cylindrical measures. Zbl 0527.28017Smolyanov, O. G. 4 1983 Diffusion and quantum dynamics of particles with position-dependent mass. Zbl 1276.82065Sakbaev, V. Zh.; Smolyanov, O. G. 4 2012 The probabilistic Feynman-Kac formula for an infinite-dimensional Schrödinger equation with exponential and singular potentials. Zbl 0940.35207Albeverio, Sergio; Khrennikov, Andrew; Smolyanov, Oleg 4 1999 Exact master equations describing reduced dynamics of the Wigner function. Zbl 1151.81351Kupsch, J.; Smolyanov, O. G. 3 2008 Change of measures and their logarithmic derivatives under smooth transformations. Zbl 0836.60003Smolyanov, Oleg G.; von Weizsäcker, Heinrich 3 1995 Feynman formulas for solutions of the Schrödinger equation on compact Riemannian manifolds. Zbl 0995.58023Smolyanov, O. G.; Truman, A. 3 2000 Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators. Zbl 1436.35336Smolyanov, O. G.; Shamarov, N. N. 3 2019 Bogolyubov transformations in Wiener-Segal-Fock space. Zbl 1046.81059Kupsch, J.; Smolyanov, O. G. 3 2000 Wiener surface measures on trajectories in Riemannian manifolds. Zbl 1197.58009Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O.; Sidorova, N. A. 3 2002 Change of variable formulas for Feynman pseudomeasures. Zbl 1024.28012Smolyanov, O. G.; Truman, A. 3 1999 Locally convex spaces of vector-valued distributions with multiplicative structures. Zbl 1058.46018Khrennikov, A. Yu.; Shelkovich, V. M.; Smolyanov, O. G. 3 2002 Information entropy in problems of classical and quantum statistical mechanics. Zbl 1206.82054Kozlov, V. V.; Smolyanov, O. G. 3 2006 Functional integrals. (Kontinual’nye integraly.) Zbl 0746.46043Smol’yanov, O. G.; Shavgulidze, E. T. 3 1990 Representations of solutions of Lindblad equations by randomized Feynman formulas. Zbl 1341.81036Obrezkov, O. O.; Smolyanov, O. G. 3 2016 Nonstationary Kolmogorov probability models describing quantum measurements. Zbl 1327.81033Smolyanov, O. G.; Khrennikov, A. Yu. 3 2006 Wigner measures and quantum control. Zbl 1321.81030Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 3 2015 Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent. Zbl 1361.81057Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T. 3 2016 A simple proof of the Tarieladze’s theorem on the sufficiency of positively sufficient topologies. Zbl 0770.60004Smolyanov, O. G.; Shavgulidze, E. T. 3 1992 Noether’s theorem for dissipative quantum dynamical semi-groups. Zbl 1311.81161Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G. 3 2015 Surface measures on trajectories in Riemannian manifolds generated by diffusions. Zbl 1052.58037Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O.; Sidorova, N. A. 3 2001 Feynman path integral corresponding to the Schrödinger stochastic equation. Zbl 1065.81564Belavkin, V. P.; Smolyanov, O. G. 3 1998 Representation of regularized traces of operators by functional integrals. Zbl 1263.47058Sadovnichii, V. A.; Smolyanov, O. G.; Shavgulidze, E. T. 3 2012 Real and functional analysis. Zbl 1466.26002Bogachev, Vladimir I.; Smolyanov, Oleg G. 11 2020 Stochastic processes on the group of orthogonal matrices and evolution equations describing them. Zbl 1466.60093Zamana, K. Yu.; Sakbaev, V. Zh.; Smolyanov, O. G. 2 2020 Feynman formulas and the law of large numbers for random one-parameter semigroups. Zbl 1447.81026Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 5 2019 Randomized Hamiltonian mechanics. Zbl 1428.81080Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 4 2019 Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators. Zbl 1436.35336Smolyanov, O. G.; Shamarov, N. N. 3 2019 Hamiltonian approach to secondary quantization. Zbl 1410.81029Kozlov, V. V.; Smolyanov, O. G. 2 2018 Two theorems on isomorphisms of measure spaces. Zbl 1445.54017Kozlov, V. V.; Smolyanov, O. G. 1 2018 Topological vector spaces and their applications. Translated from the Russian. Expanded and revised translation, originally published 2012. Zbl 1378.46001Bogachev, V. I.; Smolyanov, O. G. 25 2017 Feynman formulas for nonlinear evolution equations. Zbl 1458.46030Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 3 2017 Measures on the Hilbert space of a quantum system. Zbl 1373.81040Khrennikov, Andrei Yu.; Smolyanov, O. G. 2 2017 Noether theorems and quantum anomalies. Zbl 1366.81260Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 1 2017 Relationship between the Itô-Schrödinger and Hudson-Parthasarathy equations. Zbl 1366.81214Obrezkov, O. O.; Smolyanov, O. G. 1 2017 Unbounded random operators and Feynman formulae. Zbl 1422.47049Orlov, Yurii N.; Sakbaev, Vsevolod Zh.; Smolyanov, Oleg G. 26 2016 Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions. Zbl 1335.81103Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G. 9 2016 Representations of solutions of Lindblad equations by randomized Feynman formulas. Zbl 1341.81036Obrezkov, O. O.; Smolyanov, O. G. 3 2016 Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent. Zbl 1361.81057Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T. 3 2016 Transformations of Feynman path integrals and generalized densities of Feynman pseudomeasures. Zbl 1351.81077Garsía-Naranjo, L. C.; Montaldi, J.; Smolyanov, O. G. 2 2016 Analogues of Feynman formulas for ill-posed problems associated with the Schrödinger equation. Zbl 1372.35353Sakbaev, V. G.; Smolyanov, O. G. 2 2016 Representations of regularized determinants of exponentials of differential operators by functional integrals. Zbl 1347.47024Sadovnichii, V. A.; Smolyanov, O. G.; Shavgulidze, E. T. 1 2016 Invariant and quasi-invariant measures on infinite-dimensional spaces. Zbl 1367.46037Kozlov, V. V.; Smolyanov, O. G. 4 2015 Quantum anomalies and logarithmic derivatives of Feynman pseudomeasures. Zbl 1341.81038Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 4 2015 Wigner measures and quantum control. Zbl 1321.81030Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 3 2015 Noether’s theorem for dissipative quantum dynamical semi-groups. Zbl 1311.81161Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G. 3 2015 Hamiltonian structures in the quantum theory of Hamilton-Dirac systems. Zbl 1337.81086Ratiu, T. S.; Smolyanov, O. G. 1 2015 Wigner quantization of Hamilton-Dirac systems. Zbl 1337.81082Ratiu, T. S.; Smolyanov, O. G. 1 2015 Feynman formulas as a method of averaging random Hamiltonians. Zbl 1304.81082Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 27 2014 Non-Gaussian Lagrangian Feynman-Kac formulas. Zbl 1304.81086Sakbaev, V. Z.; Smolyanov, O. G.; Shamarov, N. N. 7 2014 Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems. Zbl 1295.81097Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 7 2014 Transformations of measures via their generalized densities. Zbl 1322.46029Montaldi, J.; Smolyanov, O. G. 5 2014 Hamiltonian functional integrals representing regularized traces of higher-order differential operators. Zbl 1306.47055Sadovnichii, V. A.; Smolyanov, O. G.; Shavgulidze, E. T. 1 2014 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143Ratiu, T. S.; Smolyanov, O. G. 9 2013 Feynman formulas for stochastic and quantum dynamics of particles in multidimensional domains. Zbl 1280.81049Smolyanov, O. G.; Tolstyga, D. S. 6 2013 Schrodinger type semigroups via Feynman formulae and all that. Zbl 1354.47030Smolyanov, O. G. 5 2013 Diffusion and quantum dynamics on graphs. Zbl 1283.47050Sakbaev, V. Zh.; Smolyanov, O. G. 3 2013 Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G. 13 2012 Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian. Zbl 1280.81046Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G. 8 2012 Hamiltonian aspects of quantum theory. Zbl 1260.81092Kozlov, V. V.; Smolyanov, O. G. 7 2012 Diffusion and quantum dynamics of particles with position-dependent mass. Zbl 1276.82065Sakbaev, V. Zh.; Smolyanov, O. G. 4 2012 Representation of regularized traces of operators by functional integrals. Zbl 1263.47058Sadovnichii, V. A.; Smolyanov, O. G.; Shavgulidze, E. T. 3 2012 A Burgers-Zeldovich model for the formation of planetesimals via Nelson’s stochastic mechanics. Zbl 1260.85042Durran, Richard; Neate, Andrew; Truman, Aubrey; Smolyanov, Oleg 1 2012 Linear and nonlinear liftings of states of quantum systems. Zbl 1264.81066Amosov, G. G.; Sakbaev, V. Zh.; Smolyanov, O. G. 1 2012 Feynman-Kac and Feynman formulas for infinite-dimensional equations with Vladimirov operator. Zbl 1251.35181Smolyanov, O. G.; Shamarov, N. N.; Kpekpassi, M. 8 2011 Feynman formulas and path integrals for some evolution semigroups related to \(\tau\)-quantization. Zbl 1311.58006Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G. 7 2011 Hamiltonian Feynman formulas for equations containing the vladimirov operator with variable coefficients. Zbl 1248.35242Smolyanov, O. G.; Shamarov, N. N. 6 2011 Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G. 5 2011 Wigner measures on infinite-dimensional spaces and the Bogolyubov equations for quantum systems. Zbl 1236.81143Kozlov, V. V.; Smolyanov, O. G. 5 2011 Feynman description of the one-dimensional dynamics of particles whose masses piecewise continuously depend on coordinates. Zbl 1241.81077Smolyanov, Oleg G.; Tolstyga, D. S.; von Weizsäcker, Heinrich 5 2011 Lagrangian Feynman formulas for second-order parabolic equations in bounded and unbounded domains. Zbl 1204.47096Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G. 14 2010 Feynman formulae for Feller semigroups. Zbl 1213.47047Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L. 11 2010 Dynamics of a quantum particle with discontinuous position-dependent mass. Zbl 1200.81054Sakbaev, V. G.; Smolyanov, O. G. 6 2010 Hamiltonian Feynman integrals for equations with the Vladimirov operator. Zbl 1210.46061Smolyanov, O. G.; Shamarov, N. N. 4 2010 Infinite-dimensional equation Liouville with respect to measures. Zbl 1210.37046Kozlov, V. V.; Smolyanov, O. G. 4 2010 The Gough-James model for quantum feedback networks in Belavkin’s representation. Zbl 1218.81071Smolyanov, O. G.; Truman, A. 1 2010 Generalized Lévy Laplacians and Cesàro means. Zbl 1261.46034Accardi, L.; Smolyanov, O. G. 9 2009 Feynman formulas and path integrals for evolution equations with the Vladimirov operator. Zbl 1180.81069Smolyanov, O. G.; Shamarov, N. N. 8 2009 Feynman formulae for evolutionary equations. Zbl 1173.58006Smolyanov, Oleg G. 8 2009 Feynman formulas generated by self-adjoint extensions of the Laplacian. Zbl 1175.81106Smolyanov, O. G.; von Weizsäcker, H. 6 2009 Generalized Kolmogorov models for probabilistic quantum-type experiments. Zbl 1180.81008Smolyanov, O. G.; Khrennikov, A. Yu. 1 2009 Change of variable formulas for integrals over superspaces. Zbl 1182.81053Smolyanov, O. G.; von Weizsäcker, H. 1 2009 Generalized Wiener-Segal-Fock representations and Feynman formulae. Zbl 1175.81144Kupsch, J.; Smolyanov, O. G. 1 2009 Representation of solutions to evolution equations with Vladimirov operator in terms of Feynman path integrals. Zbl 1175.81145Smolyanov, O. G.; Shamarov, N. N. 1 2009 Feynman formulas for particles with position-dependent mass. Zbl 1159.35426Gadella, M.; Smolyanov, O. G. 17 2008 Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator. Zbl 1185.35351Smolyanov, O. G.; Shamarov, N. N. 8 2008 Feynman formula for a class of second-order parabolic equations in a bounded domain. Zbl 1218.81037Butko, Ya. A.; Grothaus, M.; Smolyanov, O. G. 8 2008 Exact master equations describing reduced dynamics of the Wigner function. Zbl 1151.81351Kupsch, J.; Smolyanov, O. G. 3 2008 Modified Lévy Laplacians. Zbl 1186.46043Gomez, F.; Smolyanov, O. G. 2 2008 Representation of solutions to a heat conduction equation with Vladimirov’s operator by functional integrals. Zbl 1304.81112Smolyanov, O. G.; Shamarov, N. N. 1 2008 Chernoff’s theorem and discrete time approximations of Brownian motion on manifolds. Zbl 1107.58014Smolyanov, Oleg G.; von Weizsäcker, Heinrich; Wittich, Olaf 43 2007 Surface measures and initial boundary value problems generated by diffusions with drift. Zbl 1156.58014Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 13 2007 Classical and nonclassical Levy Laplacians. Zbl 1155.35482Accardi, L.; Smolyanov, O. G. 7 2007 Wigner function and diffusion in a collision-free medium of quantum particles. Zbl 1120.82005Kozlov, V. V.; Smolyanov, O. G. 6 2007 Feynman formulas for evolution equations with Levy Laplacians on manifolds. Zbl 1143.35101Accardi, L.; Smolyanov, O. G. 2 2007 Weak convergence of states in quantum statistical mechanics. Zbl 1151.82324Kozlov, V. V.; Smolyanov, O. G. 1 2007 Infinite-dimensional Schrödinger equations with polynomial potentials and Feynman path integrals. Zbl 1327.81257Smolyanov, O. G.; Shavgulidze, E. T. 9 2006 Feynman formulas for evolution equations with Lévy Laplacians on infinite-dimensional manifolds. Zbl 1327.58033Accardi, L.; Smolyanov, O. G. 8 2006 Information entropy in problems of classical and quantum statistical mechanics. Zbl 1206.82054Kozlov, V. V.; Smolyanov, O. G. 3 2006 Nonstationary Kolmogorov probability models describing quantum measurements. Zbl 1327.81033Smolyanov, O. G.; Khrennikov, A. Yu. 3 2006 Surface integrals in Riemannian spaces and Feynman formulas. Zbl 1327.58015Smolyanov, O. G.; von Weizsaecker, H.; Wittich, O. 1 2006 Randomized Hamiltonian Feynman integrals and Schrödinger-Itô stochastic equations. Zbl 1133.35109Gough, J.; Obrezkov, O. O.; Smolyanov, O. G. 7 2005 Kolmogorov probability spaces describing accardi models of quantum correlations. Zbl 1082.81023Khrennikov, Andrei; Smolyanov, O. G.; Truman, A. 6 2005 Reduced dynamics of subsystems of quantum systems with quadratic Hamiltonians. Zbl 1200.81101Kupsch, J.; Smolyanov, O. G. 1 2005 Construction of diffusions on sets of mappings from an interval to compact Riemannian manifolds. Zbl 1272.60055Smolyanov, O. G.; von Weizsaecker, H.; Wittich, O. 1 2005 Probabilistic measurement models with noncommuting and commuting observables. Zbl 1272.81018Smolyanov, O. G.; Khrennikov, A. Yu. 1 2005 The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold. Zbl 1046.58014Sidorova, Nadezda A.; Smolyanov, Oleg G.; von Weizsäcker, Heinrich; Wittich, Olaf 11 2004 Complex Gâteaux differentiability, and continuity. Zbl 1082.46031Smolyanov, O. G.; Shkarin, S. A. 2 2004 The Feynman formula for the Cauchy problem in domains with boundary. Zbl 1246.81092Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 1 2004 Chernoff’s theorem and the construction of semigroups. Zbl 1057.47044Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O. 7 2003 Lévy Laplacian acting on operators. Zbl 1142.47362Accardi, L.; Querdiane, H.; Smolyanov, O. G. 6 2003 The Feynman formulas for solving infinite-dimensional Schrödinger equations with polynomial potentials. Zbl 1247.81244Smolyanov, O. G.; Shavgulidze, Eugene T. 4 2003 Asymptotic decoherence in infinite-dimensional quantum systems with quadratic Hamiltonians. Zbl 1026.81026Kupsch, J.; Smolyanov, O. G. 2 2003 Feynman integrals over trajectories in Riemannian manifolds. Zbl 1125.58010Smolyanov, O. G.; Truman, A. 2 2003 Schrödinger quantization of Hamilton-Dirac systems and Feynman integrals over superspaces. Zbl 1282.35318Albeverio, S; Smolyanov, O. G. 1 2003 A nonclassical Kolmogorov-type model describing quantum experiments. Zbl 1112.81334Smolyanov, O. G.; Khrennikov, A. Yu. 1 2003 Time operators for one parameter semigroups. Zbl 1106.47302Smolyanov, O. G.; Shkarin, S. A. 1 2003 Hamiltonian Feynman path integrals via the Chernoff formula. Zbl 1060.58009Smolyanov, O. G.; Tokarev, A. G.; Truman, A. 71 2002 Lévy–Laplace operators in functional rigged Hilbert spaces. Zbl 1033.35134Accardi, L.; Smolyanov, O. G. 4 2002 Wiener surface measures on trajectories in Riemannian manifolds. Zbl 1197.58009Smolyanov, O. G.; von Weizsäcker, H.; Wittich, O.; Sidorova, N. A. 3 2002 Locally convex spaces of vector-valued distributions with multiplicative structures. Zbl 1058.46018Khrennikov, A. Yu.; Shelkovich, V. M.; Smolyanov, O. G. 3 2002 Multiplicative structures in the linear space of vector-valued distributions. Zbl 1223.46043Smolyanov, O. G.; Khrennikov, A. Yu.; Shelkovich, V. M. 2 2002 Probabilistic models of quantum systems, and Bell type inequalities. Zbl 1034.81006Smolyanov, O. G.; Truman, A. 1 2002 ...and 77 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 374 Authors 93 Smolyanov, Oleg Georgievich 32 Sakbaev, Vsevolod Zhanovich 19 Orlov, Yurii N. 18 Bogachev, Vladimir Igorevich 17 Khrennikov, Andreĭ Yur’evich 15 Shamarov, Nikolaĭ Nikolaevich 13 Kinderknecht, Yana A. 12 Remizov, Ivan D. 11 Bentkus, Vidmants-Kastytis 11 von Weizsäcker, Heinrich 10 Accardi, Luigi 10 Ratiu, Tudor Stefan 10 Volkov, Boris O. 8 Gough, John E. 7 Albeverio, Sergio A. 7 Kozlov, Valeriĭ Vasil’evich 6 Borisov, Leonid Andreevich 6 Kupsch, Joachim 6 Obrezkov, Oleg O. 6 Serovaĭskiĭ, Simon Ya. 6 Wittich, Olaf 5 Grothaus, Martin 5 Kumanogo, Naoto 5 Romanov, Volodymyr A. 5 Rybakov, Konstantin Aleksandrovich 5 Schilling, René Leander 5 Shavgulidze, Eugene T. 4 Bogdansky, Yu. V. 4 Kalinichenko, Artem A. 4 Kravtseva, A. K. 4 Léandre, Rémi 4 Norin, N. V. 4 Rguigui, Hafedh 4 Tolstyga, D. S. 4 Truman, Aubrey 4 Volovich, Igor’ Vasil’evich 4 Zavadsky, D. V. 3 Dubravina, V. A. 3 Ferrando, Juan Carlos 3 Ji, Un Cig 3 Kislitsyn, A. A. 3 Kozyrev, Sergeĭ Vladimirovich 3 Lobanov, S. G. 3 Loboda, Alexander A. 3 Massam, Helene M. 3 Mayer-Wolf, Eduardo 3 Mazzucchi, Sonia 3 Montaldi, James A. 3 Plyashechnik, A. S. 3 Sadovnichiĭ, Viktor Antonovich 3 Shkarin, Stanislav A. 3 Smolyanova, M. O. 3 Sukhinin, M. F. 2 Arutyunyan, Lavrentin Martunovich 2 Barhoumi, Abdessatar 2 Burkatskii, M. O. 2 Chasco, María Jesús 2 Chen, Linghua 2 Coifman, Ronald Raphaël 2 Daletskii, Alexei 2 Dürr, Detlef 2 Efremova, Lyudmila S. 2 Fonseca-Mora, Christian A. 2 Fuhrman, Marco 2 Gao, Tingran 2 García-Garrido, Víctor J. 2 Garola, Claudio 2 Glöckner, Helge 2 Grekhneva, A. D. 2 Hamilton, Eugene P. 2 Jakobsen, Espen Robstad 2 Kaminskij, V. A. 2 Kirillov, A. I. 2 Kolb, Martin 2 Konderla, T. 2 Kosov, Egor D. 2 Kurapin, G. I. 2 Kurbyko, I. F. 2 Kuzemsky, Alexander Leonidovich 2 Mamon, Sergeĭ Vladimirovich 2 Martin Peinador, Elena 2 Nashed, M. Zuhair 2 Nel, Louis Daniel 2 Ouerdiane, Habib 2 Panyunin, N. M. 2 Papatriantafillou, Maria H. 2 Penot, Jean-Paul 2 Račkauskas, Alfredas Yurgevich 2 Saitô, Kimiaki 2 Sakbaev, V. G. 2 Schechter, Martin 2 Shamarova, Èvelina Yur’evna 2 Shapiro, Alexander 2 Sharp, Bernice 2 Shelkovich, Vladimir M. 2 Sidorova, Nadia 2 Smolentsev, Nicolai Konstantinovich 2 Soraggi, Roberto Luiz 2 Stan, Aurel Iulian 2 Tarasenko, P. Yu. ...and 274 more Authors all top 5 Cited in 128 Serials 67 Mathematical Notes 63 Doklady Mathematics 34 Infinite Dimensional Analysis, Quantum Probability and Related Topics 26 Russian Journal of Mathematical Physics 26 Journal of Mathematical Sciences (New York) 15 Ukrainian Mathematical Journal 14 Journal of Functional Analysis 12 Proceedings of the Steklov Institute of Mathematics 11 Journal of Mathematical Physics 10 Journal of Mathematical Analysis and Applications 9 International Journal of Theoretical Physics 9 Lithuanian Mathematical Journal 9 Theoretical and Mathematical Physics 8 Lobachevskii Journal of Mathematics 6 Siberian Mathematical Journal 6 Russian Mathematics 5 Moscow University Mathematics Bulletin 5 Potential Analysis 5 Applied and Computational Harmonic Analysis 4 Bulletin of the Australian Mathematical Society 4 Journal of Geometry and Physics 4 Bulletin des Sciences Mathématiques 4 Izvestiya: Mathematics 4 Nonlinear Analysis. 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New Series 1 Advances in Computational Mathematics 1 Journal of Difference Equations and Applications 1 Bernoulli ...and 28 more Serials all top 5 Cited in 55 Fields 150 Quantum theory (81-XX) 148 Functional analysis (46-XX) 125 Probability theory and stochastic processes (60-XX) 105 Operator theory (47-XX) 101 Partial differential equations (35-XX) 71 Measure and integration (28-XX) 71 Global analysis, analysis on manifolds (58-XX) 22 Ordinary differential equations (34-XX) 19 Dynamical systems and ergodic theory (37-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 18 Statistical mechanics, structure of matter (82-XX) 16 Mechanics of particles and systems (70-XX) 14 Statistics (62-XX) 11 Real functions (26-XX) 11 General topology (54-XX) 11 Systems theory; control (93-XX) 10 Topological groups, Lie groups (22-XX) 10 Differential geometry (53-XX) 10 Operations research, mathematical programming (90-XX) 8 Numerical analysis (65-XX) 8 Fluid mechanics (76-XX) 7 Computer science (68-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Category theory; homological algebra (18-XX) 5 Several complex variables and analytic spaces (32-XX) 4 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 4 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 4 Algebraic topology (55-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Nonassociative rings and algebras (17-XX) 3 Group theory and generalizations (20-XX) 3 Abstract harmonic analysis (43-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 2 Integral equations (45-XX) 2 Manifolds and cell complexes (57-XX) 2 Relativity and gravitational theory (83-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year