Journal of Lie Theory 34 (2024), No. 3, 577--594
Copyright Heldermann Verlag 2024
A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2
Piotr Graczyk
LAREMA, Université d'Angers, Angers, France
piotr.graczyk@univ-angers.fr
Patrice Sawyer
Laurentian University, Sudbury, Canada
psawyer@laurentian.ca
We transform a formula for the A2 Dunkl kernel by Béchir Amri. The resulting formula expresses the A2 Dunkl kernel in terms of the A1 Dunkl kernel involving only positive terms. This result allows us to derive sharp estimates for the A2 Dunkl kernel. As an interesting by-product, we obtain sharp estimates for the corresponding heat kernel.
Keywords: Dunkl kernel, sharp estimate, root system.
MSC: 33E30; 17B22, 20F55.
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