Fourier transforms related to a root system of rank 1

Wolter Groenevelt

Fourier transforms related to a root system of rank 1

Representation Theory 2007-06-13 v1 Classical Analysis and ODEs

Authors: Wolter Groenevelt

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.

Keywords

fourier transforms root system of rank 1 difference-reflection operators double affine hecke algebra dunkl-cherednik operator wilson polynomials

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@article{arxiv.math/0511079,
  title  = {Fourier transforms related to a root system of rank 1},
  author = {Wolter Groenevelt},
  journal= {arXiv preprint arXiv:math/0511079},
  year   = {2007}
}

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32 pages

Fourier transforms related to a root system of rank 1

Abstract

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