An operator-theoretic proof of an estimate on the transfer operator
type: Item
instance of: scholarly article
title: An operator-theoretic proof of an estimate on the transfer operator
zbMATH Open document ID: 0946.47026
author: Stéphane Descombes
author: Boun Oumar Dia
published in: Journal of Functional Analysis
publication date: 2000-10-17T00:00:00Z
review text: The authors address the question: How fast the Trotter-Kato type product formula \[ [\exp(tV/2n)\exp(-t\Delta/n)\exp(tV/2n)]^n \] converges to \(\exp\{(-\Delta +V)\}\)? Here \(\Delta\) is a Laplacian on \(R^N\) and \(V\) is a potential. Using operator techniques they prove a fine estimate in terms of \(L^2\)-operator norm convergence and some smoothness conditions on \(V\). Similar estimations were obtained by \textit{T. Ichinose} and \textit{S. Takanobu} [Nagoya Math. J. 149, 53-81 (1998; Zbl 0917.47041)] using probabilistic methods.
reviewed by: Robert Alicki
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D08
zbMATH DE Number: 1319962
zbMATH Keywords: Feynman-Kac semigroups
zbMATH Keywords: Trotter-Kato type product formula
MaRDI profile type: Publication
full work available at URL: jfan.1999.3412
OpenAlex ID: W1986269644
cites work: Commutateurs de certains semi-groupes holomorphes et applications aux directions alternées
cites work: An estimate of the Kac transfer operator
cites work: Error bounds on exponential product formulas for Schrödinger operators
cites work: Q4853528
cites work: Q4886208
cites work: Q4896564
cites work: Introduction to spectral theory. With applications to Schrödinger operators
cites work: Estimate of the difference between the Kac operator and the Schrödinger semigroup
cites work: The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases
cites work: Error estimate in operator norm for Trotter-Kato product formula
cites work: Q4269463
cites work: Q5526485
cites work: Q3909512
cites work: \(L^ p\) estimates for Schrödinger operators with certain potentials
DOI: 10.1006/JFAN.1999.3412
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description: scientific article; zbMATH DE number 1319962