A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2023 English Publisher:MathDoc/Centre MersenneJournal:Journal of Lie Theory, volume 34, pages 577-594 (eissn: 0949-5932,

Copyright policy )

Authors: Graczyk, Piotr; Sawyer, Patrice;

doi: 10.5802/jolt.1350 , 10.48550/arxiv.2308.01388

arXiv: 2308.01388

A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2

- Summary
- Subjects
- Metrics

Abstract

In this paper, we transform a formula for the $A_2$ Dunkl kernel by Béchir 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.

Keywords

Orthogonal polynomials and functions associated with root systems, sharp estimate, Reflection and Coxeter groups (group-theoretic aspects), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary 33E30, Secondary 17B22, 20F55, Other functions coming from differential, difference and integral equations, Dunkl kernel, root system, Root systems, Representation Theory (math.RT), Mathematics - Representation Theory, Heat kernel

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

0

Average

Green