Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T09:53:04.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion on Lie Groups

Published online by Cambridge University Press:  20 November 2018

N. TH. Varopoulos
N. TH. Varopoulos*
Affiliation:
Université de Paris VI 4 Place Jussieu 75005 Paris France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The heat kernel of an amenable Lie group satisfies either pt ~ exp(—ct1/3) or pt ~ t-a as t → ∞. We give a condition on the Lie algebra which characterizes the two cases.

Résumé

Résumé

Pour le noyau de la chaleur sur un groupe de Lie moyennable on a soit pt ~ exp(—ct1/3), soit pt ~ t-a (lorsque t → ∞). On donne une condition sur l'algèbre de Lie qui caractérise les deux cas

Keywords

22E3043A8060J6060J65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 438 - 448
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Varopoulos, N. Th., Analysis on Lie groups, 1. Funct. Anal. 76 (1988), 346–410.Google Scholar
2. Varopoulos, N. Th., Saloff-Coste, L. and Coulhon, T., Analysis and Geometry on groups, Cam. Univ. Press, 1992.Google Scholar
3. Hormander, L., Hypoelliptic second order operators, Acta Math. 119(1967), 147–171.Google Scholar
4. Varadarajan, V. S., Lie groups, Lie algebras and their representations, Prentice-Hall.Google Scholar
5. Reiter, H., Classical harmonic analysis and locally compact groups, Oxford Math. Monograph, 1968.Google Scholar
6. Varopoulos, N. Th., Potential Theory on non unimodulargroups, Harmonic Analysis and discrete Potential Theory, Plenum (1992), to appear.Google Scholar
7. Varopoulos, N. Th., Small Time Gaussian Estimates of Heat Diffusion Kernels, II: The Theory of Large Deviations, J. Funct. Analysis 93(1990), 1–33.Google Scholar
8. Varopoulos, N. Th., A Potential Theoretic Property of Soluble Groups, Bull. Sc. Math, 2e série 108(1983), 263–273.Google Scholar
9. Alexopoulos, G., Fonctions harmoniques bornées sur les groupes résolubles, C.R. Acad. Sci. Paris 305 (1987), 777–779.Google Scholar
10. Alexopoulos, G.,A lower estimate for central probability on polycyclic groups, Can. J. Math. 44(1992), 897–910.Google Scholar
11. Varopoulos, N. Th., Groups of sup erpolynomial growth, Proceedings of the I.C.M. satellite conference on Harmonic Analysis, Springer Verlag, 1991.Google Scholar