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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… (More)

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… (More)

A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the… (More)

In this note a class of second-order parabolic equations with variable coefficients, depending on coordinate, is considered in bounded and unbounded domains. Solutions of the Cauchy–Dirichlet and the… (More)

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… (More)

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… (More)

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… (More)

The classical Chernoff Theorem is a statement about the convergence of discrete-time approximations of semigroups using a family of contraction operators strongly differentiable at t = 0. By… (More)

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… (More)