An uncertainty principle and sampling inequalities in Besov spaces

TL;DR

This paper extends an uncertainty principle to Besov spaces, providing bounds on function traces on discrete sets and exploring applications to irregular sampling in these spaces.

Contribution

It generalizes Strichartz's uncertainty principle from Sobolev to Besov spaces and establishes sampling inequalities for irregular sampling scenarios.

Findings

Derived lower bounds for function traces in Besov spaces.

Extended results to multivariate Besov spaces.

Discussed applications to irregular sampling in critical Besov spaces.

Abstract

We extend Strichartz's uncertainty principle [18] from the setting of the Sobolov space W 1,2 (R) to more general Besov spaces B 1/p p,1 (R). The main result gives an estimate from below of the trace of a function from the Besov space on a uniformly distributed discrete subset. We also prove the corresponding result in the multivariate case and discuss some applications to irregular approximate sampling in critical Besov spaces.