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HEAT KERNEL BOUNDS, POINCARÉ SERIES, AND L2 SPECTRUM FOR LOCALLY SYMMETRIC SPACES

Part of: Global differential geometry Partial differential equations on manifolds; differential operators Parabolic equations and systems

Published online by Cambridge University Press:  01 August 2008

ANDREAS WEBER
ANDREAS WEBER*
Affiliation:
Institut für Algebra und Geometrie, Universität Karlsruhe (TH), Englerstr. 2, 76128 Karlsruhe, Germany (email: andreas.weber@math.uni-karlsruhe.de)
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Abstract

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We derive upper Gaussian bounds for the heat kernel on complete, noncompact locally symmetric spaces M=Γ∖X with nonpositive curvature. Our bounds contain the Poincaré series of the discrete group Γ and therefore we also provide upper bounds for this series.

Keywords

heat kernelslocally symmetric spacesPoincaré series

MSC classification

Secondary: 58J35: Heat and other parabolic equation methods 35K05: Heat equation 53C35: Symmetric spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 73 - 86
Copyright
Copyright © 2008 Australian Mathematical Society

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