Modulation Preserving Operators 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 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.2010 Mathematics Subject Classification. Primary 47A15 ; Secondary 42B99, 22B99.