Norms of Modes and Quasi-modes revisited
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
This is a partly expository, partly new paper on sup norm estimates of eigenfunctions. The focus is on the quantum completely integrable case. We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded eigenfunctions' (Duke Math J. 111 (2002), 97-132), based on the analysis of quasi-modes and Birkhoff normal forms. We also discuss related issues of resonant normal forms and tunnelling between tori.
Keywords
Cite
@article{arxiv.math/0202074,
title = {Norms of Modes and Quasi-modes revisited},
author = {John A. Toth and Steve Zelditch},
journal= {arXiv preprint arXiv:math/0202074},
year = {2007}
}
Comments
A conference talk at the June 2001 Mt. Holyoke conference in harmonic analysis