Individual stability of \(C_0\)-semigroups with uniformly bounded local resolvent
type: Item
instance of: scholarly article
title: Individual stability of \(C_0\)-semigroups with uniformly bounded local resolvent
zbMATH Open document ID: 0892.47040
DOI: 10.1007/BF02574130
author: Jan van Neerven
published in: Semigroup Forum
publication date: 1998-07-20T00:00:00Z
full work available at URL: https://eudml.org/doc/135479
review text: In the spirit of \textit{L. Gearhart}'s theorem [Trans. Am. Math. Soc. 236, 385-394 (1978; Zbl 0371.47033)] the author proves the following individual stability theorem for strongly continuous semigroups \((T(t))\) on a Banach space X with generator A. If, for some \(x_0 \in X\), the map \(z \mapsto R(z,A)x_0\) has a bounded analytic extension to \(\{z:\text{Re}z > 0\}\) then \(\| T(t)R(\lambda, A)x_0\| \leq M(1 + t)\) for all \(t\geq 0\), some (all) \(\lambda \in \varrho(A)\) and some \(M \in \mathbb R_+\). As a corollary he obtains the recent theorem by \textit{L. Weis} and \textit{V. Wrobel} [Proc. Am. Math. Soc. 124, No. 12, 3663-3671 (1996; Zbl 0863.47027)].
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 936963
zbMATH Keywords: \(C_0\)-semigroups
zbMATH Keywords: individual stability
zbMATH Keywords: uniformly bounded local resolvent
reviewed by: Rainer Nagel
MaRDI profile type: Publication
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OpenAlex ID: W2104784358
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description: scientific article; zbMATH DE number 936963