Journal of Lie Theory

no. 3
A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2
Journal of Lie Theory, Volume 34 (2024) no. 3, pp. 577-594
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.
DOI: 10.5802/jolt.1350
Classification: 33E30, 17B22, 20F55
Keywords: Dunkl kernel, sharp estimate, root system 
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     author = {P. Graczyk and P. Sawyer},
     title = {A {Formula} and {Sharp} {Estimates} for the {Dunkl} {Kernel} for the {Root} {System} {A\protect\textsubscript{2}}},
     journal = {Journal of Lie Theory},
     pages = {577--594},
     year = {2024},
     volume = {34},
     number = {3},
     doi = {10.5802/jolt.1350},
     zbl = {1551.33012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1350/}
}
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P. Graczyk; P. Sawyer. A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2. Journal of Lie Theory, Volume 34 (2024) no. 3, pp. 577-594. doi: 10.5802/jolt.1350

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