Complete Interpolating sequences for small Fock Spaces

TL;DR

This paper characterizes complete interpolating sequences for a class of small Fock spaces, extending classical results and answering a question about perturbations of Riesz bases of complex exponentials.

Contribution

It provides a new characterization of complete interpolating sequences for small Fock spaces, analogous to Kadets-Ingham's theorem, and addresses an open question in the field.

Findings

Characterization of complete interpolating sequences for small Fock spaces.

Extension of Kadets-Ingham's $1/4$-Theorem to this setting.

Resolution of an open question by Baranov et al. about perturbations of Riesz bases.

Abstract

We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_\varphi,\ 1\leq p<\infty$, where $\varphi(z)=\alpha\left(\log^+|z|\right)^2,\ \alpha>0$. 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}.