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 $widehat{G}$‎. ‎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.