Shift-invariant sampling in two-sided small Fock spaces

TL;DR

This paper characterizes shift-invariant sampling sequences in two-sided small Fock spaces, providing a geometric description applicable across the full range of p, from 0 to infinity.

Contribution

It introduces a geometric framework for shift-invariant sampling sequences in small Fock spaces, extending understanding across all p-values.

Findings

Characterization of shift-invariant sampling sequences

Geometric description applicable for all p in (0, ∞]

Extension of sampling theory in Fock spaces

Abstract

We consider the sampling problem for two-sided small Fock spaces $\mathcal{F}^p_{\alpha}$, for the full range $0 < p \le \infty$. We establish a geometric description of shift-invariant sampling sequences, i.e., sequences $\Lambda$ such that $c \Lambda$ is sampling for all $c \in \mathbb{C} \setminus \{ 0 \}$.