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The $L^{p}$ spectrum and heat dynamics of locally symmetric spaces of higher rank

Published online by Cambridge University Press:  30 June 2014

LIZHEN JI  and
ANDREAS WEBER
LIZHEN JI
Affiliation:
Department of Mathematics, University of Michigan, 1834 East Hall, Ann Arbor, MI 48109-1043, USA email lji@umich.edu
ANDREAS WEBER
Affiliation:
Institut für Algebra und Geometrie, KIT, Kaiserstraße 89–93, 76128 Karlsruhe, Germany email andreasweber.mail@gmail.com
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Abstract

The aim of this paper is to study the spectrum of the $L^{p}$ Laplacian and the dynamics of the $L^{p}$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the $L^{p}$ heat semigroup on $M$ has a certain chaotic behavior if $p\in (1,2)$, whereas for $p\geq 2$ such chaotic behavior never occurs.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 5 , August 2015 , pp. 1524 - 1545
Copyright
© Cambridge University Press, 2014 

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