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Riesz bases of reproducing kernels in small Fock spaces

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
dc.contributor.authorOMARI, Youssef
dc.date.accessioned2024-04-04T02:58:50Z
dc.date.available2024-04-04T02:58:50Z
dc.date.created2020-02-01
dc.date.issued2020
dc.identifier.issn1069-5869
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192691
dc.description.abstractEnWe give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces $\mathcal{F}^2_{\varphi}$, the spaces of entire functions $f$ such that $f\mathrm{e}^{-\varphi} \in L^{2}(\mathbb{C})$, where $\varphi(z)= (\log^+|z|)^{\beta+1}$, $0< \beta \leq 1$.The first results in this direction are due to Borichev-Lyubarskii who showed that $\varphi$ with $\beta=1$ is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov-Dumont-Hartman-Kellay in the case when $\beta=1$. The present paper answers a question in Baranov et al. by extending their results for all parameters $\beta\in (0,1)$. Our results are analogous to those obtained for the case $\beta=1$ and those proved for Riesz bases of complex exponentials for the Paley-Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enRiesz bases of reproducing kernels in small Fock spaces
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1911.11001
bordeaux.journalJournal of Fourier Analysis and Applications
bordeaux.volume26
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01918516
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01918516v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Journal%20of%20Fourier%20Analysis%20and%20Applications&amp;rft.date=2020&amp;rft.volume=26&amp;rft.issue=1&amp;rft.eissn=1069-5869&amp;rft.issn=1069-5869&amp;rft.au=KELLAY,%20Karim&amp;OMARI,%20Youssef&amp;rft.genre=article


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