On integrated semigroups which are not exponentially bounded
type: Item
instance of: scholarly article
title: On integrated semigroups which are not exponentially bounded
zbMATH Open document ID: 0812.47041
author: Isao Miyadera
author: Masashi Okubo
author: Naoki Tanaka
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-04-24T00:00:00Z
review text: Using the Laplace transform methods, the theory of exponentially bounded \(\alpha\)-times integrated semigroups was introduced and studied by H. Kellermann, W. Arendt and M. Hieber. In this article the authors treated the notion of \(\alpha\)-times integrated semigroups, which are not exponentially bounded on a Banach space \(X\). It should be noted that the Laplace transform techniques are not available in this case. Some properties of \(\alpha\)-times integrated semigroups and characterization of their generators are given. As an application, a bounded perturbation result of \(\alpha\)-times integrated semigroups and an adjoint theorem is proved.
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 556452
zbMATH Keywords: Laplace transform
zbMATH Keywords: exponentially bounded \(\alpha\)-times integrated semigroups
zbMATH Keywords: generators
zbMATH Keywords: adjoint theorem
reviewed by: A. Rhandi
MaRDI profile type: Publication
full work available at URL: pjaa.69.199
OpenAlex ID: W2011304719
cites work: Vector-valued Laplace transforms and Cauchy problems
cites work: Q4010828
cites work: Q3254057
cites work: Laplace Transforms and α-Times Integrated Semigroups
cites work: Integrated semigroups
cites work: Local C -Semigroups and Local Integrated Semigroups
cites work: ``Integrated semigroups'' and integrated solutions to abstract Cauchy problems
DOI: 10.3792/PJAA.69.199
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description: scientific article; zbMATH DE number 556452