Korean J. Math.  Vol 28, No 4 (2020)  pp.649-671
DOI: https://doi.org/10.11568/kjm.2020.28.4.649

The Cherednik and the Gaussian Cherednik Windowed transforms on $\mathbb{R}^d$ in the W-invariant case

Amina Hassini, Khalifa Trimeche

Abstract


In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on $\mathbb{R}^d$, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on $\mathbb{R}^d$ in the W-invariant case.

Keywords


The Cherednik wavelets; Cherednik operators; The Cherednik windowed transform; The Gaussian Cherednik Wavelets; The Gaussian Cherednik windowed transform.

Subject classification

33C67; 51F15; 33E30; 43A32; 44A15.

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