Titre : Formules explicites du noyau de la chaleur sur les espaces projectifs des quaternions 

Auteurs : Ali Hafoud ,  Allal Ghanmi,  

Revue : Avancées en Mathématiques Pures et Appliquées 

Numéro : Numéro 2 (Mars 2022) 

Volume : 13 

Date : 2022/03/14 

DOI : 10.21494/ISTE.OP.2022.0809 

ISSN : 1869-6090 

Résumé : We consider the heat equation on the quaternionic projective space $$$P_{n}(ℍ)$$$, and we establish two formulas for the heat kernel, a series expansion involving Jacobi polynomials, and an integral representation involving a $$$\theta$$$-function. More precisely, using the quaternonic Hopf fibration and the explicit integral representation of the heat kernel on the complex projective space $$$P_{2n+1}(ℂ)$$$, as well as an integral representation of Jacobi polynomials in terms of Gegenbauer polynomials, we give an explicit integral representation of the heat kernel on the $$$n$$$-quaternionic projective space. We also establish an explicit series expansion of the heat kernel in terms of the Jacobi polynomials. Moreover, we derive an explicit formula of the heat kernel on the sphere $$$S^4$$$. 

Éditeur : ISTE OpenScience