Oversampling and undersampling in de Branges spaces arising from regular Schr\"odinger operators

TL;DR

This paper extends classical oversampling and undersampling theories from Paley-Wiener spaces to de Branges spaces associated with regular Schr"odinger operators, broadening the understanding of sampling in these advanced function spaces.

Contribution

It generalizes sampling theorems to de Branges spaces linked to regular Schr"odinger operators, incorporating a wide class of potentials.

Findings

Generalization of oversampling and undersampling results

Application to de Branges spaces from Schr"odinger operators

Broader class of potentials considered

Abstract

The classical results on oversampling and undersampling (or aliasing), of functions in Paley-Wiener spaces, are generalized to the case of functions in de Branges spaces arising from regular Schr\"odinger operators with a wide range of potentials.