Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials

DOI10.1080/00036811.2010.502117zbMath1216.33040arXiv1006.1140OpenAlexW3103192611WikidataQ58279812 ScholiaQ58279812MaRDI QIDQ2995539

Fethi Bouzeffour, Koornwinder, Tom H.

Publication date: 21 April 2011

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.1140

zbMATH Keywords

Dunkl-Cherednik operatorvector-valued polynomialsnon-symmetric Jacobi polynomialsnonsymmetric little \(q\)-Jacobi polynomialspositive-definite inner product

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items

Charting the 𝑞-Askey scheme, Unnamed Item, Dualities in the q‐Askey Scheme and Degenerate DAHA, Nonsymmetric Askey-Wilson polynomials and \(Q\)-polynomial distance-regular graphs, Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials, Meixner matrix ensembles, Dunkl shift operators and Bannai-Ito polynomials

Cites Work

• Harmonic analysis associated with the Jacobi-Dunkl operator on \(-\frac{\pi}{2},\frac{\pi}{2}[\)]
• Nonsymmetric Koornwinder polynomials and duality
• Harmonic analysis for certain representations of graded Hecke algebras
• An elementary approach to the hypergeometric shift operators of Opdam
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group