Shift-invariant sampling in two-sided small Fock spaces

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