On Wiener's Lemma on locally compact abelian groups
Classical Analysis and ODEs
2025-05-16 v1 Complex Variables
Functional Analysis
Abstract
We establish a general form of Wiener's lemma for measures on locally compact abelian (LCA) groups by using Fourier analysis and the theory of F{{\o}}lner sequences. Our approach provides a unified framework that that encompasses both the discrete and continuous cases. We also show a version of Wiener's lemma for Bochner-Riesz means on both R^d and T^d . Mathematics Subject Classification (2010). 43A25.
Keywords
Cite
@article{arxiv.2505.10061,
title = {On Wiener's Lemma on locally compact abelian groups},
author = {Philippe Jaming and Karim Kellay and Rolando Perez},
journal= {arXiv preprint arXiv:2505.10061},
year = {2025}
}