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.
Publié le : 1999-07-05
Classification:
Green function,
heat kernel,
Iwasawa AN groups,
Poisson semigoup,
reductive Lie groups,
semisimple Lie groups,
spherical functions,
symmetric spaces (Riemannian,
noncompact),
22E30, 22E46, 31C12, 43A80, 43A85, 43A90, 58G11,
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
@article{hal-00022962,
author = {Anker, Jean-Philippe and Ji, Lizhen},
title = {Heat kernel and Green function estimates on noncompact symmetric spaces},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00022962}
}
Anker, Jean-Philippe; Ji, Lizhen. Heat kernel and Green function estimates on noncompact symmetric spaces. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00022962/