Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Abstract

In this paper, we study a class of pseudodifferential operators known as timefrequency localization operators, which depend on a symbol ς and two windows functions g1 and g2. We first present some basic properties of the windowed Opdam-Cherednik transform. Then, we use modulation spaces associated with the Opdam-Cherednik transform as appropriate classes for symbols and windows, and study the boundedness and compactness of the localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten-von Neumann class.