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Article: The expansion of a semigroup and a Riesz basis criterion
Title | The expansion of a semigroup and a Riesz basis criterion |
---|---|
Authors | |
Keywords | Heat Exchanger Equation Riesz Basis Semigroup Expansion |
Issue Date | 2005 |
Publisher | Academic 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? |
Abstract | Problems 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 Identifier | http://hdl.handle.net/10722/156123 |
ISSN | 2023 Impact Factor: 2.4 2023 SCImago Journal Rankings: 2.046 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Xu, GQ | en_US |
dc.contributor.author | Yung, SP | en_US |
dc.date.accessioned | 2012-08-08T08:40:29Z | - |
dc.date.available | 2012-08-08T08:40:29Z | - |
dc.date.issued | 2005 | en_US |
dc.identifier.citation | Journal Of Differential Equations, 2005, v. 210 n. 1, p. 1-24 | en_US |
dc.identifier.issn | 0022-0396 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156123 | - |
dc.description.abstract | Problems 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.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jde | en_US |
dc.relation.ispartof | Journal of Differential Equations | en_US |
dc.subject | Heat Exchanger Equation | en_US |
dc.subject | Riesz Basis | en_US |
dc.subject | Semigroup Expansion | en_US |
dc.title | The expansion of a semigroup and a Riesz basis criterion | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yung, SP:spyung@hkucc.hku.hk | en_US |
dc.identifier.authority | Yung, SP=rp00838 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/j.jde.2004.09.015 | en_US |
dc.identifier.scopus | eid_2-s2.0-12344275684 | en_US |
dc.identifier.hkuros | 98093 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-12344275684&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 210 | en_US |
dc.identifier.issue | 1 | en_US |
dc.identifier.spage | 1 | en_US |
dc.identifier.epage | 24 | en_US |
dc.identifier.isi | WOS:000226770000001 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Xu, GQ=7404263948 | en_US |
dc.identifier.scopusauthorid | Yung, SP=7006540951 | en_US |
dc.identifier.issnl | 0022-0396 | - |