Pointwise bounds for $L^2$ eigenfunctions on locally symmetric spaces

Mathematics – Spectral Theory

Scientific paper

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17 pp

Scientific paper

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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