On Beurling's sampling theorem in $\R^n$

TL;DR

This paper provides an elementary proof of Beurling's sampling theorem, establishing a sufficient condition for sampling multi-dimensional band-limited functions, which is fundamental in signal processing and harmonic analysis.

Contribution

The paper offers a simplified, elementary proof of Beurling's theorem for multi-dimensional functions, enhancing understanding and potential applications.

Findings

Elementary proof of Beurling's sampling theorem

Sufficient condition for sampling in multiple dimensions

Improved accessibility of the theorem's proof

Abstract

We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.