Geodesic
The Heat Equation on the Spaces of Positive Definite Matrices
Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 624-651

Voir la notice de l'article provenant de la source Cambridge University Press

The main topic of this paper is the study of the fundamental solution of the heat equation for the symmetric spaces of positive definite matrices, Pos(n,R).Our first step is to develop a “False Abel Inverse Transform” which transforms functions of compact support on an euclidean space into integrable functions on the symmetric space. The transform is shown to satisfy the relation is the usual Laplacian with a constant drift).Using this transform, we find explicit formulas for the heat kernel in the cases n = 2 and n = 3. These formulas allow us to give the asymptotic development for the heat kernel as t tends to infinity. Finally, we give an upper and lower bound of the same type for the heat kernel.
DOI : 10.4153/CJM-1992-038-7
Mots-clés : 58G30, (53C35,58G11) 
Sawyer, P. The Heat Equation on the Spaces of Positive Definite Matrices. Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 624-651. doi: 10.4153/CJM-1992-038-7
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