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Article: Properties of a class of C0 semigroups on Banach spaces and their applications

TitleProperties of a class of C0 semigroups on Banach spaces and their applications
Authors
Xu, GQYung, SP
KeywordsC0 semigroups
Compactness
Differentiability
Expansion
Wave equation
Issue Date2007
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaa
Citation
Journal Of Mathematical Analysis And Applications, 2007, v. 328 n. 1, p. 245-256 How to Cite?
DOI: http://dx.doi.org/10.1016/j.jmaa.2006.05.050
AbstractIn this paper we investigate some properties of a class of C0 semigroups on Banach spaces. Suppose that the spectrum of the infinitesimal generator is discrete and there are only finitely many eigenvalues in each vertical strip, we show that such semigroups can be expanded by their generalized eigenvectors under certain conditions. As a consequence, we assert that the semigroups with these conditions are eventually differentiable provided that the system of generalized eigenvectors is complete. As an example, we apply our results to a one-dimensional wave control system. © 2006 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/54300
ISSN
0022-247X
2021 Impact Factor: 1.417
2020 SCImago Journal Rankings: 0.951
ISI Accession Number ID
WOS:000243800100018
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorXu, GQen_HK
dc.contributor.authorYung, SPen_HK
dc.date.accessioned2009-04-03T07:42:36Z-
dc.date.available2009-04-03T07:42:36Z-
dc.date.issued2007en_HK
dc.identifier.citationJournal Of Mathematical Analysis And Applications, 2007, v. 328 n. 1, p. 245-256en_HK
dc.identifier.issn0022-247Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/54300-
dc.description.abstractIn this paper we investigate some properties of a class of C0 semigroups on Banach spaces. Suppose that the spectrum of the infinitesimal generator is discrete and there are only finitely many eigenvalues in each vertical strip, we show that such semigroups can be expanded by their generalized eigenvectors under certain conditions. As a consequence, we assert that the semigroups with these conditions are eventually differentiable provided that the system of generalized eigenvectors is complete. As an example, we apply our results to a one-dimensional wave control system. © 2006 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaaen_HK
dc.relation.ispartofJournal of Mathematical Analysis and Applicationsen_HK
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectC0 semigroupsen_HK
dc.subjectCompactnessen_HK
dc.subjectDifferentiabilityen_HK
dc.subjectExpansionen_HK
dc.subjectWave equationen_HK
dc.titleProperties of a class of C0 semigroups on Banach spaces and their applicationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022-247X&volume=328&issue=1&spage=245&epage=256&date=2007&atitle=Properties+of+a+class+of+C_0+semigroups+on+Banach+spaces+and+their+applicationsen_HK
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_HK
dc.identifier.authorityYung, SP=rp00838en_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1016/j.jmaa.2006.05.050en_HK
dc.identifier.scopuseid_2-s2.0-33845888546en_HK
dc.identifier.hkuros136671-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33845888546&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume328en_HK
dc.identifier.issue1en_HK
dc.identifier.spage245en_HK
dc.identifier.epage256en_HK
dc.identifier.isiWOS:000243800100018-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridXu, GQ=7404263948en_HK
dc.identifier.scopusauthoridYung, SP=7006540951en_HK
dc.identifier.issnl0022-247X-

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