Formulas for q-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators
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We study the spectral problem associated to a Ruijsenaars-type (q-)difference version of the one-dimensional Schrödinger operator with Pöschl–Teller potential. The eigenfunctions are constructed explicitly with the aid of the inverse scattering theory of reflectionless Jacobi operators. As a result, we arrive at combinatorial formulas for basic hypergeometric deformations of zonal spherical functions on odd-dimensional hyperboloids and spheres.
KeywordsSpectral Problem Spherical Function Inverse Scattering Scattering Theory Jacobi Operator
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