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Transmutation kernels for the little q-Jacobi function transform

Erik Koelink·Hjalmar Rosengren
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Abstract

The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel (a kind of non-symmetric Poisson kernel) relating little q-Jacobi function transforms for different parameter sets. A product formula for the dual transmutation kernel is obtained. For the inverse transform the transmutation kernel is given as a 3\phi2-series, and a product formula as a finite sum is derived. The transmutation kernel gives rise to intertwining operators for the second order hypergeometric q-difference operator, which generalise the intertwining operators arising from a Darboux factorisation.

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BibTeXRIS

Erik Koelink, Hjalmar Rosengren. 2000-11-01. Transmutation kernels for the little q-Jacobi function transform. https://arxiv.org/abs/math/0011002

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