arXiv subjects
Publications and source records attributed to Y. Omari.
We characterize zero sets for which every subset remains a zero set too in the Fock space $\mathcal{F}^p$, $1\leq p<\infty$. We are also interested in the study of a stability problem for some examples of uniqueness set with zero excess in Fock spaces.
In the present work, we are interested in compact integration operators $I_g f(z) = \int_0^z f(ζ)g'(ζ)dζ$ acting on the Hardy space $H^2$ and on the weighted Bergman spaces $\mathcal{A}^2_α$. We give upper and lower estimates for the singular values of $I_g$.
We prove that zero sets for distinct Fock spaces are not the same, this is an answer of a question asked by K. Zhu in \cite[Page. 209]{Zhu}.
We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_φ,\ 1\leq p<\infty$, where $φ(z)=α\left(\log^+|z|\right)^2,\ α>0$. Our results are {analogous} to the classical Kadets-Ingham's $1/4-$Theorem on perturbation of Riesz bases of complex exponentials, and they answer a question asked by A. Baranov, A. Dumont, A. Hartmann and K. Kellay in \cite[page 31]{baranov2015sampling}.
A Gabor system in $L^2(\mathbb{R})$, generated by a window $g\in L^2(\mathbb{R})$ and associated with a sequence of times and frequencies $Γ\subset\mathbb{R}^2$, is a set formed by translations in time and modulations of $g$. In this paper we consider the case when $g$ is the Gaussian function and $Γ$ is a sequence whose associated Gabor system $\mathcal{G}_Γ$ is complete and minimal in $L^2(\mathbb{R})$. We consider two main cases: that of the lattice without one point and that of the sequence constructed by Ascensi, Lyubarskii and Seip lying on the union of the coordinate axes of the time-frequency space. We study the stability problem for these two systems. More precisely, we describe the perturbations of $Γ$ such that the associated Gabor systems remain to be complete and minimal. Our method of proof is based essentially on estimates of some infinite products.