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

TL;DR

This paper investigates the properties of localization operators linked to the windowed Opdam-Cherednik transform, focusing on their boundedness, compactness, and Schatten class membership within modulation spaces.

Contribution

It introduces a new class of localization operators based on the windowed Opdam-Cherednik transform and analyzes their boundedness, compactness, and Schatten class properties on modulation spaces.

Findings

Localization operators are bounded and compact on modulation spaces.

These operators belong to the Schatten-von Neumann class.

The study extends the theory of pseudodifferential operators in time-frequency analysis.

Abstract

In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol $\varsigma$ and two windows functions $g_1$ and $g_2$. 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.