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

Amina Hassini, Rayaane Maalaoui, Khalifa Trimeche

Abstract


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.

Keywords


Heckman-Opdam theory, Wavelets; Generalized wavelet transform.

Subject classification

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

Sponsor(s)



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