Evolution systems and perturbations of generators of strongly continuous groups
type: Item
instance of: scholarly article
title: Evolution systems and perturbations of generators of strongly continuous groups
zbMATH Open document ID: 1083.47031
published in: Journal of Evolution Equations
publication date: 2005-04-29T00:00:00Z
review text: The author considers a problem of unbounded perturbation of a \(C_0\)-group in a Banach space. The author proves firstly that if \(A\) generates a \(C_0\)-group in a Banach space and \(B\) is unbounded, then an extension of \(A+B\) generates a \(C_0\)-semigroup if and only if the family of operator \(\{e^{-rA}Be^{r A}\}_{r\geq 0}\) has an appropriate evolution system. From this result, the author then deduces some sufficient conditions for a perturbation of group generators to generate a semigroup. In particular, the Trotter product formula is obtained again.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 2163359
zbMATH Keywords: unbounded perturbation
zbMATH Keywords: \(C_0\)-group
zbMATH Keywords: evolution system
author: R. deLaubenfels
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
full work available at URL: s00028-004-0050-5
OpenAlex ID: W1991255747
DOI: 10.1007/S00028-004-0050-5
description: scientific article; zbMATH DE number 2163359