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Article: The expansion of a semigroup and a Riesz basis criterion

TitleThe expansion of a semigroup and a Riesz basis criterion
Authors
KeywordsHeat Exchanger Equation
Riesz Basis
Semigroup Expansion
Issue Date2005
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jde
Citation
Journal Of Differential Equations, 2005, v. 210 n. 1, p. 1-24 How to Cite?
AbstractProblems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. Suppose that A is the generator of a C0 semigroup on a Hilbert space and σ (A) = σ1 (A) ∪ σ2 (A) with σ2 (A) is consisted of isolated eigenvalues distributed in a vertical strip. It is proved that if σ2 (A) is separated and for each λ ∈ σ2 (A), the dimension of its root subspace is uniformly bounded, then the generalized eigenvectors associated with σ2 (A) form an ℒ-basis. Under different conditions on the Riesz projection, the expansion of a semigroup is studied. In particular, a simple criterion for the generalized eigenvectors forming a Riesz basis is given. As an application, a heat exchanger problem with boundary feedback is investigated. It is proved that the heat exchanger system is a Riesz system in a suitable state Hilbert space. © 2004 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156123
ISSN
2015 Impact Factor: 1.821
2015 SCImago Journal Rankings: 2.809
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorXu, GQen_US
dc.contributor.authorYung, SPen_US
dc.date.accessioned2012-08-08T08:40:29Z-
dc.date.available2012-08-08T08:40:29Z-
dc.date.issued2005en_US
dc.identifier.citationJournal Of Differential Equations, 2005, v. 210 n. 1, p. 1-24en_US
dc.identifier.issn0022-0396en_US
dc.identifier.urihttp://hdl.handle.net/10722/156123-
dc.description.abstractProblems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. Suppose that A is the generator of a C0 semigroup on a Hilbert space and σ (A) = σ1 (A) ∪ σ2 (A) with σ2 (A) is consisted of isolated eigenvalues distributed in a vertical strip. It is proved that if σ2 (A) is separated and for each λ ∈ σ2 (A), the dimension of its root subspace is uniformly bounded, then the generalized eigenvectors associated with σ2 (A) form an ℒ-basis. Under different conditions on the Riesz projection, the expansion of a semigroup is studied. In particular, a simple criterion for the generalized eigenvectors forming a Riesz basis is given. As an application, a heat exchanger problem with boundary feedback is investigated. It is proved that the heat exchanger system is a Riesz system in a suitable state Hilbert space. © 2004 Elsevier Inc. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jdeen_US
dc.relation.ispartofJournal of Differential Equationsen_US
dc.subjectHeat Exchanger Equationen_US
dc.subjectRiesz Basisen_US
dc.subjectSemigroup Expansionen_US
dc.titleThe expansion of a semigroup and a Riesz basis criterionen_US
dc.typeArticleen_US
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_US
dc.identifier.authorityYung, SP=rp00838en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.jde.2004.09.015en_US
dc.identifier.scopuseid_2-s2.0-12344275684en_US
dc.identifier.hkuros98093-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-12344275684&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume210en_US
dc.identifier.issue1en_US
dc.identifier.spage1en_US
dc.identifier.epage24en_US
dc.identifier.isiWOS:000226770000001-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridXu, GQ=7404263948en_US
dc.identifier.scopusauthoridYung, SP=7006540951en_US

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