Modulation invariant spaces on‎ ‎locally compact abelian groups

Document Type : Original Article

Authors

Mahdi Mortazavizadeh ¹

Reihaneh Raisi Tousi ²

¹ Ferdowsi university of Mashhad

² Ferdowsi University of Mashhad

10.22034/kjm.2020.230232.1827

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.

Keywords

locally compact abelian group‎

‎modulation invariant space‎

‎range function‎

‎modulation metric

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