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Sampling, interpolation and Riesz bases in small Fock spaces

hal.structure.identifierDepartment of Mathematics and Mechanics
dc.contributor.authorBARANOV, Anton
hal.structure.identifierInstitut de Mathématiques de Marseille [I2M]
dc.contributor.authorDUMONT, André
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHARTMANN, Andreas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
dc.date.accessioned2024-04-04T03:20:05Z
dc.date.available2024-04-04T03:20:05Z
dc.date.created2015
dc.date.issued2015
dc.identifier.issn0021-7824
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194561
dc.description.abstractEnWe give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the situation in Paley--Wiener spaces, a link can be established between Riesz bases in the Hilbert case and corresponding complete interpolating sequences in small Fock spaces with associated uniform norm. These results allow to show that if a sequence has a density stricly different from the critical one then either it can be completed or reduced to a complete interpolating sequence. In particular, this allows to give necessary and sufficient conditions for interpolation or sampling in terms of densities.
dc.language.isoen
dc.publisherElsevier
dc.subject.enRiesz bases
dc.subject.ensmall Fock spaces
dc.subject.enSampling
dc.subject.eninterpolation
dc.subject.ende Branges spaces
dc.subject.enBari's theorem
dc.title.enSampling, interpolation and Riesz bases in small Fock spaces
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1406.1152
bordeaux.journalJournal de Mathématiques Pures et Appliquées
bordeaux.page1358-1389
bordeaux.volume103
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue6
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01001761
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01001761v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Math%C3%A9matiques%20Pures%20et%20Appliqu%C3%A9es&rft.date=2015&rft.volume=103&rft.issue=6&rft.spage=1358-1389&rft.epage=1358-1389&rft.eissn=0021-7824&rft.issn=0021-7824&rft.au=BARANOV,%20Anton&DUMONT,%20Andr%C3%A9&HARTMANN,%20Andreas&KELLAY,%20Karim&rft.genre=article


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