Skip to main content

Fourier transforms related to a root system of rank 1

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wolter Groenevelt.

Rights and permissions

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.

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00031-005-1124-5

Keywords

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