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Hassini, Amina,Maalaoui, Rayaane,Trimeche, Khalifa The Kangwon-Kyungki Mathematical Society 2016 한국수학논문집 Vol.24 No.2
By using the Heckman-Opdam theory on ${\mathbb{R}}^d$ given in [20], we define and study in this paper, the generalized wavelets on ${\mathbb{R}}^d$ and the generalized wavelet transform on ${\mathbb{R}}^d$, and we establish their properties. Next, we prove for the generalized wavelet transform Plancherel and inversion formulas.
Amina Hassini,Khalifa Trimeche 강원경기수학회 2020 한국수학논문집 Vol.28 No.4
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.