On Wiener's Lemma on locally compact abelian groups

Philippe Jaming, Karim Kellay, Rolando Perez Iii

Published 2025-05-15Version 1

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.