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Difference Fourier transforms for nonreduced root systems

Jasper V. Stokman
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Abstract

In the first part of the paper kernels are constructed which meromorphically extend the Macdonald-Koornwinder polynomials in their degrees. In the second part of the paper the kernels associated with rank one root systems are used to define nonsymmetric variants of the spherical Fourier transform on the quantum SU(1,1) group. Related Plancherel and inversion formulas are derived using double affine Hecke algebra techniques.

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Jasper V. Stokman. 2001-11-20. Difference Fourier transforms for nonreduced root systems. https://arxiv.org/abs/math/0111221

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