Characterization of Weyl operator in terms of Mehler–Fock transform

Abstract

In this paper, we define the windowed‐Mehler–Fock transform and introduce the corresponding Weyl transform. Further, we examine the boundedness of windowed‐Mehler–Fock transform in Lebesgue space and establish some of its fundamental properties. Also, we give the criteria of boundedness and compactness of Weyl transform in Lebesgue space.