Strang's formula for holomorphic semi-groups
type: Item
instance of: scholarly article
title: Strang's formula for holomorphic semi-groups
zbMATH Open document ID: 1030.35095
DOI: 10.1016/S0021-7824(01)01216-8
author: Stéphane Descombes
author: Michelle Schatzman
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2003-09-25T00:00:00Z
review text: In the finite-dimensional case G. Strang proved the following approximation formula \[ \|e^{-t(A+B)}-e^{-tA/2}e^{-tB}e^{-tA/2} \|= O(t^3). \] The authors prove generalizations of this formula to the case of infinite dimensional Banach and unbounded generators \(A,B\). Detailed analysis of Schrödinger operators (\(A=-\Delta, B=V(x)\)) in \(L^p({\mathbb R}^d)\), matrix Schrödinger operator and the pair of elliptic second-order operators (\(A={d\over{dx}}a{d\over{dx}}, A={d\over{dx}}b{d\over{dx}}\)) in \(L^2({\mathbb R}^d)\) is realized.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1985994
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: matrix Schrödinger operator
zbMATH Keywords: pair of elliptic second-order operators
reviewed by: Michael Perelmuter
MaRDI profile type: Publication
cites work: Convergence of a splitting method of high order for reaction-diffusion systems
cites work: An operator-theoretic proof of an estimate on the transfer operator
cites work: Q4838252
cites work: Commutateurs de certains semi-groupes holomorphes et applications aux directions alternées
cites work: An estimate of the Kac transfer operator
cites work: Q4853528
cites work: Geometric theory of semilinear parabolic equations
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 Schrödinger semigroup. II: The general case including the relativistic case
cites work: Q5526485
cites work: Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling
cites work: Error bounds for exponential operator splittings
cites work: Trotter-Kato product formula and operator-norm convergence
cites work: Fractional powers of self-adjoint operators and Trotter-Kato product formula
cites work: Stability of the Peaceman-Rachford approximation
cites work: A note on asymptotic splitting and its applications
cites work: Global error estimates for exponential splitting
cites work: Q5607484
cites work: On the Construction and Comparison of Difference Schemes
description: scientific article; zbMATH DE number 1985994