Inverse Harish-Chandra Transform and Difference Operators

Abstract

We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the coordinates are obtained as well as a simple proof of the Harish-Chandra inversion theorem using the Opdam transform.

AMSTeX

References in corpus (2)

• A recursion and a combinatorial formula for Jack polynomials
• Integrality of two variable Kostka functions

Cited by in corpus (5)

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• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions
• On a ${\mathbb{C}}^2$-valued integral index transform and bilateral hypergeometric series