# Riesz Wavelets, Tiling and Spectral Sets in LCA Groups

## TL;DR

This paper extends the theory of wavelet and Riesz wavelet sets from Euclidean spaces to infinite locally compact abelian groups, exploring their geometric properties and tiling behavior.

## Contribution

It generalizes Wang's Euclidean wavelet result to the setting of infinite locally compact abelian groups, broadening the scope of wavelet theory.

## Key findings

- Extended wavelet set properties to LCA groups
- Established tiling and spectral set relationships in LCA groups
- Generalized Euclidean wavelet results to a broader class of groups

## Abstract

This paper is devoted to the study of geometry properties of wavelet and Riesz wavelet sets on locally compact abelian groups. The catalyst for our research is a result by Wang ([32], Theorem 1.1) in the Euclidean wavelet theory. Here, we extend the result to wavelet and Riesz wavelet collection of sets in infinite locally compact abelian groups.