L^p norms of eigenfunctions in the completely integrable case
Spectral Theory
2016-11-23 v1
Abstract
The eigenfunctions e^{i \lambda x} of the Laplacian on a flat torus have uniformly bounded L^p norms. In this article, we prove that for every other quantum integrable Laplacian, the L^p norms of the joint eigenfunctions must blow up at a rate \gg \lambda^{p-2/4p - \epsilon} for every \epsilon >0 as \lambda \to \infty.
Keywords
Cite
@article{arxiv.math/0208045,
title = {L^p norms of eigenfunctions in the completely integrable case},
author = {John A. Toth and Steve Zelditch},
journal= {arXiv preprint arXiv:math/0208045},
year = {2016}
}
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19 pages