Exponential Riesz bases in non-Archimedean locally compact Abelian groups

2025/05/27 by Aihua Fan, Fan, Aihua, Shilei Fan +1
Mathematics · #43A75 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.21310

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Riesz bases of exponentials and the Bohr topology
• Riesz bases of exponentials and multi-tiling in finite abelian groups
• Riesz basis of exponentials for a union of cubes in R^d
• Unions of exponential Riesz bases
• A set with no Riesz basis of exponentials