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L p-Spectral Theory of Locally Symmetric Spaces with \(\mathbb{Q}\)-Rank One

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Abstract

We study the L p-spectrum of the Laplace–Beltrami operator on certain complete locally symmetric spaces \(M=\Gamma\backslash X\) with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.

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  1. Institut für Algebra und Geometrie, Universität Karlsruhe (TH), Englerstr. 2, 76128, Karlsruhe, Germany

    Andreas Weber

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Weber, A. L p-Spectral Theory of Locally Symmetric Spaces with \(\mathbb{Q}\)-Rank One. Math Phys Anal Geom 10, 135–154 (2007). https://doi.org/10.1007/s11040-007-9026-3

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