- Fourier transforms related to a root system of rank 1.
- Transformation Groups
- Volume | Issue number
- 12 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
- 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 nonsymmetric versions of the Wilson polynomials and the Wilson functions.
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