Shift-invariant sampling in two-sided small Fock spaces

Abstract

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