Concentration inequalities for Paley-Wiener spaces

TL;DR

This paper investigates bounds on how much of a signal's energy in Paley-Wiener spaces can be concentrated on specific sets, extending previous one-dimensional results to higher dimensions using density measures.

Contribution

It generalizes Donoho and Logan's 1992 concentration bounds from one dimension to higher dimensions in Paley-Wiener spaces.

Findings

Extended concentration bounds to higher dimensions.

Provided bounds based on set densities.

Connected results to signal processing and harmonic analysis.

Abstract

This article considers the question of how much of the mass of an element in a Paley-Wiener space can be concentracted on a given set. We seek bounds in terms of relative densities of the given set. We extend a result of Donoho and Logan from 1992 in one dimension and consider similar results in higher dimensions.