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arXiv · 2308.01388

A formula and sharp estimates for the Dunkl kernel for the root system $A_2$

P. Graczyk·P. Sawyer
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Abstract

In this paper, we transform a formula for the $A_2$ Dunkl kernel by B\'echir Amri. The resulting formula expresses the $A_2$ Dunkl kernel in terms of the $A_1$ Dunkl kernel involving only positive terms. This result allows us to derive sharp estimates for the $A_2$ Dunkl kernel. As an interesting by-product, we obtain sharp esitmates for the corresponding heat kernel.

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BibTeXRIS

P. Graczyk, P. Sawyer. 2023-08-02. A formula and sharp estimates for the Dunkl kernel for the root system $A_2$. https://arxiv.org/abs/2308.01388

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