Sonine Transform Associated to the Dunkl Kernel on the Real Line

Fethi Soltani

doi:10.3842/SIGMA.2008.092

Sonine Transform Associated to the Dunkl Kernel on the Real Line

Classical Analysis and ODEs 2008-12-31 v1

Authors: Fethi Soltani

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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 ${}^tS_{\alpha,\beta}$ .

Cite

@article{arxiv.0812.4666,
  title  = {Sonine Transform Associated to the Dunkl Kernel on the Real Line},
  author = {Fethi Soltani},
  journal= {arXiv preprint arXiv:0812.4666},
  year   = {2008}
}

Comments

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Sonine Transform Associated to the Dunkl Kernel on the Real Line

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