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arXiv · 2606.15185

The Opdam-Cherednik kernel is the Laplace transform of a positive measure

Colin McSwiggen·Siddhartha Sahi
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Abstract

We prove that the Opdam-Cherednik kernel, also known as the nonsymmetric Opdam hypergeometric function, can be written as the Laplace transform of a positive measure supported on the convex hull of the Weyl group orbit of its argument. As a consequence, the trigonometric Dunkl intertwining operator is positivity preserving. The main ingredient in the proof is a new formula for the Opdam-Cherednik kernel as a degeneration of nonsymmetric Macdonald polynomials. As a further application, we prove majorization inequalities for Macdonald polynomials and Heckman-Opdam hypergeometric functions associated with arbitrary root systems.

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Colin McSwiggen, Siddhartha Sahi. 2026-06-13. The Opdam-Cherednik kernel is the Laplace transform of a positive measure. https://arxiv.org/abs/2606.15185

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