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Heat kernel estimates and Lp-spectral theory of locally symmetric spaces

✍ Scribed by Andreas Weber

Book ID
127456594
Year
2007
Tongue
English
Weight
1 MB
Edition
disser., U.Karlsruhe
Category
Library
ISBN-13
9783866441088

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✦ Synopsis

In this work we derive upper Gaussian bounds for the heat kernel on locally symmetric spaces of non-compact type. Furthermore, we determine explicitly the Lp-spectrum of locally symmetric spaces M whose universal covering is a rank one symmetric space of non-compact type if either the fundamental group of M is small (in a certain sense) or if the fundamental group is arithmetic and M is non-compact.

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The necessary density condition in C known for sampling and interpolation in the L p space of entire functions with a subharmonic weight is extended to the case of a 2-homogeneous, plurisubharmonic weight function in C. The method is by estimating the eigenvalues of a certain Toeplitz concentration