Geodesic
Sonine Transform Associated to the Dunkl Kernel on the Real Line
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Dunkl intertwining operator $V_\alpha$ and its dual ${}^tV_\alpha$, we define and study the Dunkl Sonine operator and its dual on $\mathbb R$. Next, we introduce complex powers of the Dunkl Laplacian $\Delta_\alpha$ and establish inversion formulas for the Dunkl Sonine operator $S_{\alpha,\beta}$ and its dual ${}^tS_{\alpha,\beta}$. Also, we give a Plancherel formula for the operator ${}^tS_{\alpha,\beta}$.
Keywords: Dunkl intertwining operator; Dunkl transform; Dunkl Sonine transform; complex powers of the Dunkl Laplacian. 
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     author = {Fethi Soltani},
     title = {Sonine {Transform} {Associated} to the {Dunkl} {Kernel} on the {Real} {Line}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a91/}
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Fethi Soltani. Sonine Transform Associated to the Dunkl Kernel on the Real Line. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a91/

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