Modulation invariant spaces on locally compact abelian groups

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 $\hat{G}$. 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.

arXiv admin note: text overlap with arXiv:1910.14675, arXiv:1910.13514