Comptes Rendus
Analyse harmonique, Théorie des représentations
Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case A n
Piotr Graczyk1 ; Patrice Sawyer2 
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.

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.

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.

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DOI : 10.5802/crmath.188
Classification : 33C67, 43A90, 53C35
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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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},
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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/

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[9] Sigurdur Helgason Groups and geometric analysis: integral geometry, invariant differential operators, and spherical functions, Mathematical Surveys and Monographs, 83, American Mathematical Society, 2000 (corrected reprint of the 1984 original edition) | Zbl

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[16] Patrice Sawyer A Laplace-type representation of the generalized spherical functions associated with the root systems of type A, Mediterr. J. Math., Volume 14 (2017) no. 4, 147 | MR | Zbl

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