A Bochner Theorem for Dunkl Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• ISSN: 1815-0659
• Main Authors: Vinet, L., Zhedanov, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146799
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Bochner Theorem for Dunkl Polynomials / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ.

We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal polynomials in this category are limits of little and big q-Jacobi pol...