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Publications Influence

The various definitions of the derivative in linear topological spaces

- V. I. Averbukh, O. Smolyanov
- Mathematics
- 31 August 1968

The object of this article is to give a survey of the existing definitions of the operation of differentiation in linear topological spaces (l.t.s.) and to show the connections between them. There… Expand

111 6

Analytic properties of infinite-dimensional distributions

- V. Bogachev, O. Smolyanov
- Mathematics
- 30 June 1990

CONTENTS Introduction ??1. Notations, terminology, and auxiliary results ??2. The analytic properties of measures ??3. The properties of subspaces of differentiability ??4. The smoothness of some… Expand

86 5

The theory of differentiation in linear topological spaces

- V. I. Averbukh, O. Smolyanov
- Mathematics
- 31 December 1967

CONTENTSIntroductionChapter I. Differentiation along a subspace § 1. Definition of the first derivative § 2. Formal rules of differentiation § 3. The mean value theorem. Partial derivatives § 4.… Expand

126 4

MEASURES ON LINEAR TOPOLOGICAL SPACES

- O. Smolyanov, S. V. Fomin
- Mathematics
- 31 August 1976

This survey contains some results on measures in linear topological spaces and in completely regular topological spaces. These results are important in the theory of linear differential equations… Expand

59 3

Hamilton-Jacobi-Bellman equations for quantum optimal feedback control

- J. Gough, V. P. Belavkin, O. Smolyanov
- Physics, Mathematics
- 24 February 2005

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive… Expand

40 2- PDF

Noether’s theorem for dissipative quantum dynamical semi-groups

- J. Gough, T. Ratiu, O. Smolyanov
- Physics, Mathematics
- 28 October 2014

Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301… Expand

12 2- PDF

Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds

- O. Smolyanov, H. V. Weizsäcker, O. Wittich
- Mathematics
- 9 September 2004

Let $(S(t))_{t \ge 0}$ be a one-parameter family of positive integral operators on a locally compact space $L$. For a possibly non-uniform partition of $[0,1]$ define a finite measure on the path… Expand

86 1- PDF

Hamiltonian Feynman path integrals via the Chernoff formula

- O. Smolyanov, A. Tokarev, A. Truman
- Mathematics
- 19 September 2002

The main aim of the present paper is using a Chernoff theorem (i.e., the Chernoff formula) to formulate and to prove some rigorous results on representations for solutions of Schrodinger equations by… Expand

97 1

Ordinary differential equations in locally convex spaces

- S. Lobanov, O. Smolyanov
- Mathematics
- 30 June 1994

CONTENTS Introduction §1. Equations with continuous right-hand side 1.1. Some definitions and notation 1.2. Peano's theorem 1.3. Kneser's theorem 1.4. Continuous dependence on initial data 1.5. Joint… Expand

30 1