Fourier transforms related to a root system of rank 1
arXiv:math/0511079
Abstract
We introduce an algebra consisting of difference-reflection operators and multiplication operators that can be considered as a analogue of Sahi's double affine Hecke algebra related to the affine root system of type . We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra , and the corresponding Fourier transforms. These eigenfunctions are non-symmetric versions of the Wilson polynomials and the Wilson functions.
32 pages