Stable sampling and Fourier multipliers

Abstract

We study the relationship between stable sampling sequences for bandlimited functions in $L^p({\mathbb{R}}^n)$ and the Fourier multipliers in $L^p$. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship.

Revised version with improved presentation