1. The heat kernel on noncompact symmetric spaces
- Author
-
Anker, Jean-Philippe, Ostellari, Patrick, Anker, Jean-Philippe, S. G. Gindikin, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville (LMPA), and Université du Littoral Côte d'Opale (ULCO)
- Subjects
sous-laplacien ,principe du maximum ,010308 nuclear & particles physics ,010102 general mathematics ,espace symétrique ,transformation d'Abel ,[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] ,MSC: 22E30, 35B50, 43A85, 58J35 (22E46, 43A80, 43A90) ,[MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA] ,01 natural sciences ,noyau de la chaleur ,0103 physical sciences ,groupe de Lie semisimple ,0101 mathematics - Abstract
The heat kernel plays a central role in mathematics. It occurs in several fields: analysis, geometry and - last but not least - probability theory. In this survey, we shall focus on its analytic aspects, specifically sharp bounds, in the particular setting of Riemannian symmetric spaces of noncompact type. It is a natural tribute to Karpelevic, whose pioneer work [Ka] inspired further study of the geometry of theses spaces and of the analysis of the Laplacian thereon.
- Published
- 2003