Summary: HEAT KERNEL AND GREEN FUNCTION ESTIMATES
ON NONCOMPACT SYMMETRIC SPACES
JeanPhilippe Anker & Lizhen Ji
In memory of Carl S. Herz (19301995)
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 19941997 Network Fourier
Analysis and TMR 19982001 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 AMS-TEX
2 JEANPHILIPPE ANKER & LIZHEN JI
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 efficiently 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
needed to digest and refine the formidable work of HarishChandra and his followers.