Pointwise bounds for L² eigenfunctions on locally symmetric spaces
classification
🧮 math.SP
math.DG
keywords
boundseigenfunctionslocallypointwisespacesspectrumsymmetricbelow
read the original abstract
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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