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Fourier transforms related to a root system of rank 1

Wolter Groenevelt
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Abstract

We introduce an algebra $\mathcal H$ 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 $(C^\vee_1, C_1)$. We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra $\mathcal H$, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric versions of the Wilson polynomials and the Wilson functions.

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Wolter Groenevelt. 2005-11-03. Fourier transforms related to a root system of rank 1. https://arxiv.org/abs/math/0511079

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