For a densely defined self-adjoint operator H in Hilbert space F the operator exp⁡(− it H) is
the evolution operator for the Schrödinger equation i ψ t′= H ψ, ie if ψ (0, x)= ψ 0 (x) then ψ …

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 …

We construct the Hamiltonian Feynman, Lagrangian Feynman, and Feynman–Kac formulas
for the solution of the Cauchy problem with the Schrödinger operator− M g D α− V, where D …

The procedure of generalized averaging of random strongly continuous semigroups of linear
operators is investigated by means of Feynman-Chernoff iterations. The main features of this …

We study the long-time asymptotic behaviour of semigroups generated by non-local
Schrödinger operators of the form H=− L+ V; the free operator L is the generator of a …

This note is devoted to Feynman formulas (ie, representations of semigroups by limits of n-
fold iterated integrals as n→∞) and their connections with phase space Feynman path …

We study measures on a real separable Hilbert space E that are invariant with respect to
both shifts by arbitrary vectors of the space and orthogonal transformations. In particular, our …

Evolution semigroups generated by pseudo-differential operators are considered. These
operators are obtained by different (parameterized by a number τ) procedures of …

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is
proved that the Cauchy problem in well posed in the class of uniform limits of infinitely …

This note is devoted to the approximation of evolution semigroups generated by some
Markov processes and hence to the approximation of transition probabilities of these …