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Communications in Mathematical Physics

, Volume 210, Issue 2, pp 335–369 | Cite as

Formulas for q-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators

  • J. F. van Diejen
  • A. N. Kirillov

Abstract:

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.

Keywords

Spectral Problem Spherical Function Inverse Scattering Scattering Theory Jacobi Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. F. van Diejen
    • 1
  • A. N. Kirillov
    • 2
  1. 1.Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 1, Chile CL
  2. 2.Department of Mathematics, Hokkaido University, Sapporo 060-0810, JapanJP

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