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- W2929899099 abstract "In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and ${}^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on $mathbb{R}^d$. By using these operators we define the hypergeometric translation operator $mathcal{T}^W_x, x in mathbb{R}^d$, and its dual ${}^tmathcal{T}^W_x, x in mathbb{R}^d$, we express them in terms of the hypergeometric Fourier transform $mathcal{H}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform $mathcal{H}^W$. We study also the hypergeometric convolution product on $W$-invariant $L^p_{mathcal{A}_k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results." @default.
- W2929899099 created "2019-04-11" @default.
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- W2929899099 date "2019-03-30" @default.
- W2929899099 modified "2023-10-01" @default.
- W2929899099 title "The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$" @default.
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- W2929899099 doi "https://doi.org/10.11568/kjm.2019.27.1.221" @default.
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