Modulation invariant spaces on locally compact abelian groups

TL;DR

This paper introduces and characterizes modulation invariant spaces on locally compact abelian groups, providing a new framework for understanding their structure and topology using a range function approach.

Contribution

It defines modulation invariant spaces on locally compact abelian groups and characterizes them via a novel range function method, also exploring their topological properties.

Findings

Characterization of modulation invariant spaces using range functions

Introduction of a metric on the collection of these spaces

Analysis of topological properties of the space of modulation invariant spaces

Abstract

We define and investigate modulation invariant spaces on a locally compact abelian group $G$ with respect to a closed subgroup of the dual group $\widehat{G}$. Using a range function approach, we establish a characterization of modulation invariant spaces. Finally, we define a metric on the collection of all modulation invariant spaces and study some topological properties of the metric space.