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

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Published: Dec 30, 2020
Keywords:
The Cherednik wavelets, Cherednik operators, The Cherednik windowed transform, The Gaussian Cherednik Wavelets, The Gaussian Cherednik windowed transform.
Mathematics Subject Classification:
33C67, 51F15, 33E30, 43A32, 44A15.

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Amina Hassini
Faculty of Sciences of tunis, Department of Mathematics CAMPUS, 2092 Tunis, Tunisia
Khalifa Trimeche
Faculty of Sciences of tunis, Department of Mathematics CAMPUS, 2092 Tunis, Tunisia

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.


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