Korean J. Math. Vol. 24 No. 2 (2016) pp.235-271
DOI: https://doi.org/10.11568/kjm.2016.24.2.235

Generalized wavelets and the generalized wavelet transform on $\mathbb{R}^d$ for the Heckman-Opdam theory

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Amina Hassini
Rayaane Maalaoui
Khalifa Trimeche


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.

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