Oversampling and aliasing in de Branges spaces arising from Bessel operators

TL;DR

This paper investigates de Branges spaces linked to Bessel operators, demonstrating they exhibit oversampling and aliasing properties through generalized Fourier transforms of perturbed Bessel equations.

Contribution

It introduces a new class of de Branges spaces derived from Bessel operators and analyzes their oversampling and aliasing characteristics.

Findings

De Branges spaces from Bessel operators exhibit oversampling.

These spaces demonstrate aliasing phenomena.

Generalized Fourier transforms reveal these properties.

Abstract

We show that a class of de Branges spaces, generated by means of generalized Fourier transforms associated with perturbed Bessel differential equations, has the properties of oversampling and aliasing.