Uncertainty principles for the Opdam-Cherednik transform on modulation spaces

TL;DR

This paper extends classical uncertainty principles to the Opdam-Cherednik transform within modulation spaces, using heat kernel properties and Phragmén-Lindelöf type results to establish these foundational inequalities.

Contribution

It introduces uncertainty principles for the Opdam-Cherednik transform on modulation spaces, a novel setting for these classical inequalities.

Findings

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

Establishes Hardy's uncertainty principle in this context.

Demonstrates Morgan's uncertainty principle for the Opdam-Cherednik transform.

Abstract

In this paper, we establish the Cowling--Price's, Hardy's and Morgan's uncertainty principles for the Opdam-Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi-Cherednik operator and the versions of the Phragm{\'e}n-Lindl{\"o}f type result for the modulation spaces.