47 citations · 54 across the 10 of their papers we have counts for
13 papers
Quasi-Feynman formulas that provide fast converging Chernoff approximations to solution of parabolic differential equation on the real line
Ivan D. Remizov, Alexandr V. Vedenin
We construct explicit approximations to the solution of a second-order parabolic partial differential equation on the real line with variable coefficients. The method is based on C…
Chernoff approximations as a method for finding the resolvent of a linear operator and solving a linear ODE with variable coefficients
Ivan D. Remizov
The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linea…
Concrete examples of the rate of convergence of Chernoff approximations: numerical results for the heat semigroup and open questions on them (with appendix: full list of pictures and Python code)
K. A. Katalova, N. Nikbakht, I. D. Remizov
The article is devoted to the construction of examples that illustrate (using computer calculations) the rate of convergence of Chernoff approximations to the solution of the Cauch…
Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators
Oleg E. Galkin, Ivan D. Remizov
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…
Chernoff approximations of Feller semigroups in Riemannian manifolds
Sonia Mazzucchi, Valter Moretti, Ivan Remizov +1
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus i…
Speed of convergence of Chernoff approximations to solutions of evolution equations
A. V. Vedenin, V. S. Voevodkin, V. D. Galkin +2
This communication is devoted to establishing the very first steps in study of the speed at which the error decreases while dealing with the based on the Chernoff theorem approxima…
Formulas that represent Cauchy problem solution for momentum and position Schrödinger equation
Ivan D. Remizov
In the paper we derive two formulas representing solutions of Cauchy problem for two Schrödinger equations: one-dimensional momentum space equation with polynomial potential, and m…
Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients
Ivan D. Remizov
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 d…
Approximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)
Ivan D. Remizov
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 th…
Quasi-Feynman formulas for a Schroedinger equation with a Hamiltonian equal to a finite sum of operators
Ivan D. Remizov
In this short communication I generalize the method of obtaining quasi-Feynman formulas described in my previous paper on that topic. The theorem presented allows to obtain the sol…
Quasi-Feynman formulas -- a method of obtaining the evolution operator for the Schroedinger equation
Ivan D. Remizov
For a densely defined self-adjoint operator in Hilbert space the operator is the evolution operator for the Schrödinger equation…
Solution to a parabolic differential equation in Hilbert space via Feynman formula - parts I and II
Ivan D. Remizov
A parabolic partial differential equation is considered, where is a linear second-order differential operator with time-independent coefficients, which may…
D(Maximum)=P(Argmaximum)
Ivan D. Remizov, Alexei V. Savvateev
In this note, we propose a formula for the subdifferential of the maximum functional on the space of real-valued continuous functions defined on an arbitrary…