Stable sampling and Fourier multipliers

TL;DR

This paper explores the connection between stable sampling sequences for bandlimited functions and Fourier multipliers in L^p spaces, providing complete results for lattice sequences and partial results for irregular sequences.

Contribution

It establishes a comprehensive link between stable sampling and Fourier multipliers, especially for lattice sequences, advancing understanding in harmonic analysis.

Findings

Complete characterization for lattice sequences and fundamental domains.

Partial relationship established for irregular sampling sequences.

Enhances theoretical understanding of sampling and Fourier analysis in L^p spaces.

Abstract

We study the relationship between stable sampling sequences for bandlimited functions in $L^p(\R^n)$ 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.