Modulation preserving operators on locally compact abelian groups

TL;DR

This paper studies operators on locally compact abelian groups that preserve modulation with respect to a subgroup, providing a characterization in terms of range operators to deepen understanding of harmonic analysis structures.

Contribution

It introduces a new characterization of modulation preserving operators on locally compact abelian groups using range operators, advancing harmonic analysis theory.

Findings

Characterization of modulation preserving operators in terms of range operators

Extension of harmonic analysis tools to locally compact abelian groups

Framework for analyzing modulation invariance in abstract harmonic analysis

Abstract

Let $G$ be a locally compact abelian group and $\Lambda$ be a closed subgroup of the dual group $\widehat{G}$. In this paper, we investigate modulation preserving operators with respect to $\Lambda$, and give a characterization of them in terms of range operators.