Uncertainty principles associated with the linear canonical Dunkl transform

TL;DR

This paper extends classical uncertainty principles to the linear canonical Dunkl transform, establishing new inequalities and weighted bounds in this mathematical framework.

Contribution

It introduces analogs of key uncertainty principles and weighted inequalities specifically for the linear canonical Dunkl transform, a novel extension in harmonic analysis.

Findings

Established Miyachi, Cowling-Price, and Heisenberg-Pauli-Weyl uncertainty principles for the Dunkl transform.

Derived weighted inequalities including Nash, Clarkson, Donoho-Stark, and Matolcsi-Szucs types.

Extended the theoretical framework of harmonic analysis to the Dunkl transform setting.

Abstract

In this paper, we establish analogs of Miyachi, Cowling-Price, and Heisenberg-Pauli-Weyl uncertainty principles in the framework of the linear canonical Dunkl transform. We also obtain some weighted inequalities, such as Nash, Clarkson, Donoho-Stark, and Matolcsi-Szucs type inequalities.