L^p norms of eigenfunctions in the completely integrable case

Details L^p norms of eigenfunctions in the completely integrable case L^p norms of eigenfunctions in the completely integrable case

2002-08-06

arxiv.org/abs/math/0208045v1

Mathematics

Spectral Theory

19 pages

Scientific paper

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.

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