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Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2019

RIESZ BASES OF REPRODUCING KERNELS IN SMALL FOCK SPACES

K. Kellay
Youssef Omari
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Résumé

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.
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Dates et versions

hal-01918516 , version 1 (11-11-2018)
hal-01918516 , version 2 (24-11-2019)

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  • HAL Id : hal-01918516 , version 1

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K. Kellay, Youssef Omari. RIESZ BASES OF REPRODUCING KERNELS IN SMALL FOCK SPACES. Journal of Fourier Analysis and Applications, In press. ⟨hal-01918516v1⟩
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