Asymptotic almost periodicity and motions of semigroups of operators
type: Item
instance of: scholarly article
title: Asymptotic almost periodicity and motions of semigroups of operators
zbMATH Open document ID: 0616.47047
DOI: 10.1016/0024-3795(86)90325-3
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: In this survey, we present on overview of some of our recent work [Math. Ann. 267, 145-158 (1986; Zbl 0584.54038), Compactness in spaces of vector valued continuous functions and asymptotic almost periodicity, Math. Nachr., to appear, Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity, Dissertationes Math., to appear] in resolving certain questions that arise in a qualitative study of solutions to the abstract Cauchy problem. Focusing on motions of strongly continuous semigroups of operators and their asymptotic behavior, we address (1) the characterization of asymptotically almost periodically motions and (2) the characterization of those asymptotically almost periodic functions for which this property carries over to their integral. Moreover, we sketch our solution of the problem raised by Nemytskii and Stepanov as to when the \(\omega\)-limit set of a motion of a dynamical system is a minimal set of almost periodic motions.
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 58D07
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46A50
zbMATH DE Number: 3998601
zbMATH Keywords: solutions to the abstract Cauchy problem
zbMATH Keywords: strongly continuous semigroups of operators
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: asymptotically almost periodically motions
author: Wolfgang M. Ruess
author: William H. Summers
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90325-3
OpenAlex ID: W2049236314
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Wikidata QID: Q127725463
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description: scientific article; zbMATH DE number 3998601