Fourier transforms related to a root system of rank 1
Wolter Groenevelt
Abstract
We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q=1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C1, C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric versions of the Wilson polynomials and the Wilson functions.
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