[图书][B] Mathematical Feynman path integrals and their applications
S Mazzucchi - 2009 - World Scientific
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 …
macroscopic and the microscopic world, that is between classical and quantum mechanics …
The method of Chernoff approximation
YA Butko - Conference on Semigroups of Operators: Theory and …, 2018 - Springer
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 theorem. We outline recent results in this domain as well as clarify relations …
Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators
OE Galkin, ID Remizov - arXiv preprint arXiv:2104.01249, 2021 - arxiv.org
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 …
a wide class of differential equations. This paper studies the rate of convergence of the …
Speed of convergence of Chernoff approximations to solutions of evolution equations
AV Vedenin, VS Voevodkin, VD Galkin… - Mathematical …, 2020 - Springer
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)⊂ …
functions on X, and let L be a closed linear operator L: Dom (L)→¿ with domain Dom (L)⊂ …
Approximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)
ID Remizov - Applied Mathematics and Computation, 2018 - Elsevier
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 …
differential equation of evolution type with variable coefficients and demonstrate it on the …
Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients
ID Remizov - Journal of Mathematical Physics, 2019 - pubs.aip.org
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 …
(diffusion type) equation with variable coefficients which depend on spatial variable but do …
Compositions of Random Processes in a Hilbert Space and Its Limit Distribution
YN Orlov, VZ Sakbaev, EV Shmidt - Lobachevskii Journal of Mathematics, 2023 - Springer
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 …
processes are presented by the random linear operators acting in the space of square …
Feynman and quasi-Feynman formulas for evolution equations
ID Remizov - Doklady Mathematics, 2017 - Springer
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 …
evolution equations, ie, equations of the form ut'(t, x)= Lu (t, x), where the operator L is linear …
Direct limit of shift-invariant measures on a Hilbert space
VM Busovikov, VZ Sakbaev - Lobachevskii Journal of Mathematics, 2023 - Springer
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 …
is invariant with respect to a group of shifts along a divergence-free vector fields from wide …
[PDF][PDF] Solution of the Schrödinger equation with the use of the translation operator.
I Remizov - Mathematical Notes, 2016 - nnov.hse.ru
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 …
adjoint operator H given by the formula (Hf)(x)=(1/4) f (x)− V (x) f (x) acts on L2 (R1), and its …