Qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces

TL;DR

This paper establishes qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces, extending classical principles like Cowling-Price, Hardy, and Morgan to this new setting.

Contribution

It introduces and proves uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces, a novel extension of classical harmonic analysis results.

Findings

Proved Cowling-Price's uncertainty principle for the transform.

Established Hardy's uncertainty principle in this context.

Demonstrated Morgan's uncertainty principle for the transform.

Abstract

The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain the Cowling-Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragm{\'e}n-Lindl{\"o}f type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi-Cherednik operator.