Sonine Transform Associated to the Dunkl Kernel on the Real Line

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2008
• 1. Verfasser: Soltani, F.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2008
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147997
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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...