Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman).

DOI10.2977/prims/1145477332zbMath1108.33016arXivmath/9911163OpenAlexW2093383568MaRDI QIDQ1599150

Jasper V. Stokman, H. T. Koelink

Publication date: 15 April 2003

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911163

zbMATH Keywords

summation formulasspectral analysisspherical functionJackson integralAskey-Wilson integralAskey-Wilson functionsspherical Fourier transforms\(q\)-Jacobi functionsHaar functionalQuantum \(\text{SU}(1,1)\) groupWall functions

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of selfadjoint operator algebras to physics (46L60) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (12)

THE NONCOMMUTATIVE CHERN–CONNES CHARACTER OF THE LOCALLY COMPACT QUANTUM NORMALIZER OF SU(1,1) IN ${\rm SL}(2,\mathbb C)$ ⋮ Properties of generalized univariate hypergeometric functions ⋮ Pairings and actions for dynamical quantum groups ⋮ Non-extremal weight modules for quantized universal enveloping algebras ⋮ Towards a full solution of the large N double-scaled SYK model ⋮ Transmutation kernels for the little \(q\)-Jacobi function transform. ⋮ Connection coefficients for basic Harish-Chandra series ⋮ One-parameter orthogonality relations for basic hypergeometric series ⋮ Nevanlinna theory of the Askey-Wilson divided difference operator ⋮ Ruijsenaars' hypergeometric function and the modular double of \(\mathcal {U}_{q}(\mathfrak {sl}_{2}(\mathbb C))\) ⋮ Wilson function transforms related to Racah coefficients ⋮ An expansion formula for the Askey-Wilson function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Basic analog of Fourier series on a \(q\)-quadratic grid
• \(q\)-Laguerre polynomials and big \(q\)-Bessel functions and their orthogonality relations
• On a general \(q\)-Fourier transformation with nonsymmetric kernels
• Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
• Poids sur une \(C^ *\)-algèbre
• Recurrence relations, continued fractions, and orthogonal polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Convolutions of Orthonormal Polynomials
• A family of quantum projective spaces and related $q$-hypergeometric orthogonal polynomials
• Representations of the quantum algebra U_q(su_1,1)

This page was built for publication: Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman).