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A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator.

hal.structure.identifierMathematics, ILTPE
dc.contributor.authorGOLINSKII, Leonid
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKUPIN, Stanislas
dc.date.accessioned2024-04-04T02:22:45Z
dc.date.available2024-04-04T02:22:45Z
dc.date.created2012
dc.date.issued2012
dc.identifier.issn0022-247X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189671
dc.description.abstractEnThis is a sequel of the article by Borichev-Golinskii-Kupin [2009], where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk which satisfy certain growth hypotheses. These results were applied to get Lieb-Thirring inequalities for complex compact perturbations of a selfadjoint operator with a simply connected resolvent set. The first result of the present paper is an appropriate local version of the Blaschke-type condition from Borichev-Golinskii-Kupin [2009]. We apply it to obtain a similar condition for an analytic function in a finitely connected domain of a special type. Such condition is by and large the same as a Lieb-Thirring type inequality for complex compact perturbations of a selfadjoint operator with a finite-band spectrum. A particular case of this result is the Lieb--Thirring inequality for a selfadjoint perturbation of the Schatten class of a periodic (or a finite-band) Jacobi matrix. The latter result seems to be new in such generality even in this framework.
dc.language.isoen
dc.publisherElsevier
dc.subject.enLieb-Thirring inequality
dc.subject.enBlaschke-type condition
dc.subject.enfinite-band selfadjoint operators and their complex perturbations.
dc.subject.enfinite-band selfadjoint operators and their complex perturbations
dc.title.enA Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator.
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
bordeaux.journalJournal of Mathematical Analysis and Applications
bordeaux.page705-712
bordeaux.volume389
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00781336
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00781336v1
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