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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Groenevelt, W. Fourier transforms related to a root system of rank 1. Transformation Groups 12, 77–116 (2007). https://doi.org/10.1007/s00031-005-1124-5
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DOI: https://doi.org/10.1007/s00031-005-1124-5