The big q-Jacobi function transform
| dc.creator | Koelink, Erik | |
| dc.creator | Stokman, Jasper V. | |
| dc.date | 1999-04-21 | |
| dc.date.accessioned | 2026-07-07T05:28:46Z | |
| dc.date.available | 2026-07-07T05:28:46Z | |
| dc.description | We give a detailed description of the resolution of the identity of a second order $q$-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The $q$-difference operator and the two choices of Hilbert spaces naturally arise from harmonic analysis on the quantum group $SU_q(1,1)$ and $SU_q(2)$. The spectral analysis associated to $SU_q(1,1)$ leads to the big $q$-Jacobi function transform together with its Plancherel measure and inversion formula. The dual orthogonality relations give a one-parameter family of non-extremal orthogonality measures for the continuous dual $q^{-1}$-Hahn polynomials with $q^{-1}>1$, and explicit sets of functions which complement these polynomials to orthogonal bases of the associated Hilbert spaces. The spectral analysis associated to $SU_q(2)$ leads to a functional analytic proof of the orthogonality relations and quadratic norm evaluations for the big $q$-Jacobi polynomials. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/9904111 | |
| dc.identifier | http://arxiv.org/abs/math/9904111 | |
| dc.identifier | Constructive Approximation 19 (2003), 191-235. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78383 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 33D45, 33D80 secondary 44A20, 44A60 | |
| dc.title | The big q-Jacobi function transform | |
| dc.type | text |