Summary: HEAT KERNEL AND GREEN FUNCTION ESTIMATES
ON NONCOMPACT SYMMETRIC SPACES
Jean--Philippe Anker & Lizhen Ji
In memory of Carl S. Herz (1930--1995)
1991 Mathematics Subject Classification. 22E30, 22E46, 31C12, 43A80, 43A85, 43A90, 58G11.
Key words and phrases. Green function, heat kernel, Iwasawa AN groups, Poisson semigoup, reduc­
tive Lie groups, semisimple Lie groups, spherical functions, symmetric spaces (Riemannian, noncompact).
First author partially supported by the European Commission (HCM 1994--1997 Network Fourier
Analysis and TMR 1998--2001 Network Harmonic Analysis). Second author partially supported by the
U.S.A. National Science Foundation (postdoctoral fellowship DMS 9407427 and grant DMS 9704434)
Typeset by A M S­T E X
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2 JEAN--PHILIPPE ANKER & LIZHEN JI
1. Introduction
Let X = G/K be a noncompact Riemannian symmetric space. Although basic har­
monic analysis on X has been settled in the sixties (see [GV], [Hel2], [Hel3], for thorough
presentations of this material), it is only recently that it has been used e#ciently to pro­
duce sharp and complete results comparable to the Euclidean or the compact case ([An3],
[An5], [BOS], [CGM1], [CGM2], [MNS], [Str], ... ). The reason may be that time was

Source: Anker, Jean-Philippe - Laboratoire de Mathématiques et Applications, Physique Mathématique, Université d'Orléans

Collections: Mathematics