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 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.

References in corpus (3)

• Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
• Uncertainty principles for the Opdam-Cherednik transform on modulation spaces
• Remarks on the inverse Cherednik-Opdam transform on the real line

Cited by in corpus (3)

• Uncertainty principles for the windowed Opdam--Cherednik transform
• Qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces
• The heat semigroup associated with the Jacobi--Cherednik operator and its applications