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Fourier transforms related to a root system of rank 1


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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Correspondence to Wolter Groenevelt.

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Groenevelt, W. Fourier transforms related to a root system of rank 1. Transformation Groups 12, 77–116 (2007).

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  • Root System
  • Bilinear Form
  • Weyl Group
  • Jacobi Polynomial
  • Orthogonality Relation