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 multidimensional parabolic
(diffusion type) equation with variable coefficients which depend on spatial variable but do …

Paul Chernoff in 1968 proposed his approach to approximations of one-parameter operator
semigroups while trying to give a rigorous mathematical meaning to Feynman's path integral …

Chernoff approximations are a flexible and powerful tool of functional analysis, which can be
used, in particular, to find numerically approximate solutions of some differential equations …

In the presented paper, a research program for new vision of nanoengineering has been
suggested. In the framework of this program, growth of a solid state surface under the …

In the paper we derive two formulas representing solutions of Cauchy problem for two
Schrödinger equations: one-dimensional momentum space equation with polynomial …

The method of Chernoff approximation is a powerful and flexible tool of functional analysis
that in many cases allows expressing exp (tL) in terms of variable coefficients of linear …

Chernoff approximations of Feller semigroups and the associated diffusion processes in
Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry …

We consider the Cauchy problem for a Schrödinger equation whose Hamiltonian is the
difference of the operator of multiplication by the potential and the operator of taking the …