Heat kernel and Green function estimates on noncompact symmetric spaces
Résumé
On a noncompact symmetric space $G/K$, we obtain optimal upper and lower bounds for the heat kernel $h_t(x,y)$ (as well as asymptotics and estimates of its derivatives), under the assumption that $d(x,y)=O(1+t)$. As a consequence, we get optimal global bounds (same upper and lower bound, up to positive constants), as well as full asymptotics, for other kernels, such as the Green function. This information plays a key role in the description of the Martin compactification of $G/K$, which has been worked out recently by the second author, in collaboration with Y. Guivarc'h and J.C. Taylor.
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