A uniform approach to complete interpolating sequences for small Fock spaces with $p > 0$

TL;DR

This paper characterizes complete interpolating sequences in small Fock spaces for all p > 0, revealing a unified description for one-sided spaces and a periodicity phenomenon in two-sided spaces.

Contribution

It provides a unified perturbation-based characterization for sequences in one-sided small Fock spaces and uncovers a periodicity pattern in the sequences for two-sided spaces across different p.

Findings

Complete interpolating sequences are characterized for all p > 0.

A periodicity phenomenon is observed: sequences coincide for p=1, 2, and ∞.

Results extend previous work from p ≥ 1 to the full range 0 < p ≤ ∞.

Abstract

We study complete interpolating sequences in two types of small Fock spaces, $\mathcal{F}^p_{\alpha +}$ and $\mathcal{F}^p_{\alpha}$, for $0 < p \le \infty$. One-sided small Fock spaces $\mathcal{F}^p_{\alpha +}$ are well-studied spaces of entire functions with sub-exponential growth, while $\mathcal{F}^p_{\alpha}$ are their two-sided analogue with a symmetric singularity at the origin. For one-sided small Fock spaces $\mathcal{F}^p_{\alpha +}$, we provide a streamlined, perturbation-type description of complete interpolating sequences that unifies and extends earlier results for $1 \le p \le \infty$ to the full range $0 < p \le \infty$. For two-sided small Fock spaces $\mathcal{F}^p_{\alpha}$, we establish a parallel characterization, revealing a curious periodicity phenomenon: complete interpolating sequences for $\mathcal{F}^p_{\alpha}$ coincide exactly for $p = 1$, $p = 2$, and $p = \infty$, but differ for other $p \ge 1$.