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• W2592669893 abstract "Abstract. 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 Hilbert spaces are weighted L 2 -spaces for a discrete measure on [-1,∞) and [-1,z] , and we expand an element of the L 2 -spaces in terms of eigenfunctions of L . We establish the inversion formula by studying the spectral decomposition of L . In the first case we establish the big q -Jacobi function transform as an analogue of the Jacobi function transform. In the second case we obtain the known orthogonality relations for the big q -Jacobi polynomials. The dual orthogonality relations in the first case give a one-parameter family of nonextremal 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 corresponding weighted L 2 -spaces. The q -difference operator and the two choices of Hilbert spaces arise from the harmonic analysis on the quantum groups SU q (1,1) and SU q (2) ." @default.
• W2592669893 created "2017-03-16" @default.
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• W2592669893 date "2003-03-01" @default.
• W2592669893 modified "2023-10-18" @default.
• W2592669893 title "The Big q -Jacobi Function Transform" @default.
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• W2592669893 doi "https://doi.org/10.1007/s00365-002-0498-x" @default.
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