Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case $A_n$

Piotr Graczyk; Patrice Sawyer

doi:10.5802/crmath.188

Harmonic analysis, Representation theory

Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case

A_{n}

Piotr Graczyk ¹; Patrice Sawyer ²

¹ LAREMA, UFR Sciences, Université d’Angers, 2 bd Lavoisier, 49045 Angers cedex 01, France
² Department of Mathematics and Computer Science, Laurentian University, Sudbury, ON Canada P3E 2C6

Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 427-437.

Abstract
Résumé

In this article, we consider the radial Dunkl geometric case $k = 1$ corresponding to flat Riemannian symmetric spaces in the complex case and we prove exact estimates for the positive valued Dunkl kernel and for the radial heat kernel.

Dans cet article, nous considérons le cas géométrique radial de Dunkl $k = 1$ correspondant aux espaces symétriques riemanniens plats dans le cas complexe et nous prouvons des estimations exactes pour le noyau de Dunkl à valeur positive et pour le noyau de chaleur radial.

Received: 2020-12-21
Revised: 2021-02-09
Accepted: 2021-02-10
Published online: 2021-05-27

Zbl

DOI: 10.5802/crmath.188

Classification: 33C67, 43A90, 53C35

Author's affiliations:

Piotr Graczyk ¹; Patrice Sawyer ²

¹ LAREMA, UFR Sciences, Université d’Angers, 2 bd Lavoisier, 49045 Angers cedex 01, France
² Department of Mathematics and Computer Science, Laurentian University, Sudbury, ON Canada P3E 2C6

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Piotr Graczyk and Patrice Sawyer},
     title = {Sharp {Estimates} of {Radial} {Dunkl} and {Heat} {Kernels} in the {Complex} {Case} $A_n$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {427--437},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
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     year = {2021},
     doi = {10.5802/crmath.188},
     zbl = {07362164},
     language = {en},
}

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Piotr Graczyk; Patrice Sawyer. Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case $A_n$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 427-437. doi : 10.5802/crmath.188. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.188/

References
Cited by

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