Sonine Transform Associated to the Dunkl Kernel on the Real Line

Details Sonine Transform Associated to the Dunkl Kernel on the Real Line Sonine Transform Associated to the Dunkl Kernel on the Real Line

Publishing date

2008-12-26

URL

arxiv.org/abs/0812.4666v1

Journals

SIGMA 4 (2008), 092, 14 pages

Science

Mathematics

Field

Classical Analysis and ODEs

Additional info

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Type

Scientific paper

Digital Object Identifier

10.3842/SIGMA.2008.092

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

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