One of the most challenging problems of modern physics is the connection between the
macroscopic and the microscopic world, that is between classical and quantum mechanics …

This survey describes the method of approximation of operator semigroups, based on the
Chernoff theorem. We outline recent results in this domain as well as clarify relations …

Chernoff approximations to strongly continuous one-parameter semigroups give solutions to
a wide class of differential equations. This paper studies the rate of convergence of the …

Let X be an infinite set, let¿ be a Banach space of (not necessarily all) number-valued
functions on X, and let L be a closed linear operator L: Dom (L)→¿ with domain Dom (L)⊂ …

We present a general method of solving the Cauchy problem for a linear parabolic partial
differential equation of evolution type with variable coefficients and demonstrate it on the …

We present a general method of solving the Cauchy problem for multidimensional parabolic
(diffusion type) equation with variable coefficients which depend on spatial variable but do …

Random processes with values in an infinite dimensional linear spaces are studied. These
processes are presented by the random linear operators acting in the space of square …

New methods for obtaining representations of solutions of the Cauchy problem for linear
evolution equations, ie, equations of the form ut'(t, x)= Lu (t, x), where the operator L is linear …

A translationally invariant measure on a Hilbert space is constructed such that this measure
is invariant with respect to a group of shifts along a divergence-free vector fields from wide …

The function V is assumed to be real-valued, bounded, and measurable. Then the self-
adjoint operator H given by the formula (Hf)(x)=(1/4) f (x)− V (x) f (x) acts on L2 (R1), and its …