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This article is cited in 5 scientific papers (total in 5 papers)
Sonine Transform Associated to the Dunkl Kernel on the Real Line
Fethi Soltani Department of Mathematics, Faculty of Sciences of Tunis, Tunis-El Manar University, 2092 Tunis, Tunisia
Abstract:
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.
Received: June 19, 2008; in final form December 19, 2008; Published online December 26, 2008
Citation:
Fethi Soltani, “Sonine Transform Associated to the Dunkl Kernel on the Real Line”, SIGMA, 4 (2008), 092, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma345 https://www.mathnet.ru/eng/sigma/v4/p92
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Abstract page: | 327 | Full-text PDF : | 76 | References: | 29 |
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