Riesz bases of reproducing kernels in small Fock spaces
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KELLAY, Karim | |
| dc.contributor.author | OMARI, Youssef | |
| dc.date.accessioned | 2024-04-04T02:58:50Z | |
| dc.date.available | 2024-04-04T02:58:50Z | |
| dc.date.created | 2020-02-01 | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1069-5869 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192691 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | Riesz bases of reproducing kernels in small Fock spaces | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1911.11001 | |
| bordeaux.journal | Journal of Fourier Analysis and Applications | |
| bordeaux.volume | 26 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01918516 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01918516v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Fourier%20Analysis%20and%20Applications&rft.date=2020&rft.volume=26&rft.issue=1&rft.eissn=1069-5869&rft.issn=1069-5869&rft.au=KELLAY,%20Karim&OMARI,%20Youssef&rft.genre=article |
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