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arxiv: 1005.2980 · v1 · submitted 2010-05-17 · 🧮 math.SP · math.DG

Pointwise bounds for L² eigenfunctions on locally symmetric spaces

classification 🧮 math.SP math.DG
keywords boundseigenfunctionslocallypointwisespacesspectrumsymmetricbelow
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We prove pointwise bounds for $L^2$ eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with $\mathbb{Q}$-rank one if the corresponding eigenvalues lie below the continuous part of the $L^2$ spectrum. Furthermore, we use these bounds in order to obtain some results concerning the $L^p$ spectrum.

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