Uncertainty principles for the windowed Opdam--Cherednik transform

TL;DR

This paper explores various forms of the uncertainty principle for the windowed Opdam--Cherednik transform, establishing new inequalities and principles that extend classical results to this specific transform.

Contribution

It introduces multiple uncertainty principles for the windowed Opdam--Cherednik transform, including Heisenberg-type and Benedicks-type inequalities, expanding the theoretical framework of this transform.

Findings

Established the uncertainty principle for orthonormal sequences.

Proved Donoho--Stark's and Benedicks-type uncertainty principles.

Derived the Heisenberg-type uncertainty inequality using $k$-entropy.

Abstract

In this paper, we study a few versions of the uncertainty principle for the windowed Opdam--Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle and local uncertainty inequality for this transform. We also obtain the Heisenberg-type uncertainty inequality using the $k$-entropy of the windowed Opdam--Cherednik transform.