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

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 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 Phragmén–Lindlöf type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi–Cherednik operator.