The big \(q\)-Jacobi function transform

DOI10.1007/s00365-002-0498-xzbMath1048.33014arXivmath/9904111OpenAlexW2592669893MaRDI QIDQ1871750

Jasper V. Stokman, H. T. Koelink

Publication date: 4 May 2003

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9904111

zbMATH Keywords

Plancherel formuladifference operatorsspectral analysisbig \(q\)-Jacobi functionsbig \(q\)-Jacobi polynomialsbig \(q\)-Jacobi transform

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Linear difference operators (47B39) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (10)

Indeterminate moment problem associated with continuous dual q-Hahn polynomials ⋮ Intertwiners of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-representations and the vector-valued big q-Jacobi transform ⋮ On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials ⋮ One-parameter orthogonality relations for basic hypergeometric series ⋮ Tensor products of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-modules and the big q2-Jacobi function transform ⋮ The indeterminate moment problem for the \(q\)-Meixner polynomials ⋮ The vector-valued big \(q\)-Jacobi transform ⋮ One-dimensional double Hecke algebra and Gaussian sums ⋮ Orthogonality relations for Al-Salam-Carlitz polynomials of type II ⋮ q 2-Kampé de Fériet series and sums of continuous dual q±2-Hahn polynomials

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