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Estimations globales du noyau de la chaleur

Abstract : This thesis deals with sharp heat kernel estimates in two related settings. We consider first noncompact Riemannian symmetric spaces X = G/K, and obtain in this case the same upper and lower bound for the heat kernel associated with the Laplace-Beltrami operator L. These bounds are global in space and time. We consider next the class of sub-Laplacians on a semisimple Lie group G which induce L on the associated symmetric space X = G/K. These sub-Laplacians share properties with L: they have the same L^2 spectral gap, the associated Carnot-Carathéodory distances are all comparable with the Riemannian metric on X and, most of all, their heat kernels are all comparable (for large time) with the heat kernel on X. This yields sharp heat kernel bounds and, consequently, optimal Green Green function estimates.
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Contributor : Patrick Ostellari <>
Submitted on : Sunday, January 4, 2004 - 7:57:38 PM
Last modification on : Friday, February 26, 2021 - 3:21:58 AM
Long-term archiving on: : Friday, April 2, 2010 - 7:55:31 PM


  • HAL Id : tel-01754354, version 2



Patrick Ostellari. Estimations globales du noyau de la chaleur. Mathématiques [math]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10065⟩. ⟨tel-01754354v2⟩



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