Exponential Riesz bases in non-Archimedean locally compact Abelian groups

TL;DR

This paper investigates the existence of exponential Riesz bases in non-Archimedean locally compact Abelian groups, proving their existence for finite unions of balls and non-existence for certain bounded sets.

Contribution

It provides the first comprehensive results on the existence and non-existence of exponential Riesz bases in this class of groups.

Findings

Riesz basis of exponentials exists for all finite unions of balls

No Riesz basis of exponentials for some bounded sets

Establishes fundamental criteria for basis existence in non-Archimedean groups

Abstract

This paper establishes two fundamental results on the existence of exponential Riesz basis in non-Archimedean locally compact Abelian groups: the existence of Riesz basis of exponentials for all finite unions of balls and the non-existence of such basis for some bounded sets.