Sonine Transform Associated to the Dunkl Kernel on the Real Line

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Author: Soltani, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147997
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Sonine Transform Associated to the Dunkl Kernel on the Real Line / F. Soltani // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ.

We consider the Dunkl intertwining operator Vα and its dual tVα, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δα and establish inversion formulas for the Dunkl Sonine operator Sα,β and its dual tSα,β. Also, we give a Planch...