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Cyclicity and invariant subspaces in the Dirichlet spaces

hal.structure.identifierDépartement de Mathématiques
dc.contributor.authorEL-FALLAH, Omar
hal.structure.identifierDépartement de Mathématiques
dc.contributor.authorELMADANI, Youssef
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
dc.date.accessioned2024-04-04T03:15:25Z
dc.date.available2024-04-04T03:15:25Z
dc.date.issued2016-02-02
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194143
dc.description.abstractEnLet $\mu$ be a positive finite measure on the unit circle and $\mathcal{D} (\mu)$ the associated Dirichlet space. The generalized Brown-Shields conjecture asserts that an outer function $f \in \mathcal{D} (\mu )$ is cyclic if and only if $c_\mu (Z (f))= 0$, where $c_\mu$ is the capacity associated with $\mathcal{D} (\mu)$ and $Z(f)$ is the zero set of $f$. In this paper we prove that this conjecture is true for measures with countable support. We also give in this case a complete and explicit characterization of invariant subspaces.
dc.language.isoen
dc.title.enCyclicity and invariant subspaces in the Dirichlet spaces
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.identifier.arxiv1411.4977
bordeaux.journalJournal Functional Analysis
bordeaux.page3262-3279
bordeaux.volume270
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue9
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01084268
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01084268v1
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