Norms of Modes and Quasi-modes revisited

2002/02/08 by John A. Toth, Steve Zelditch, Toth, John A. +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Geometry and complex manifolds #Quantum chaos and dynamical systems #math-ph #math.AP #math.MP #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0202074

A conference talk at the June 2001 Mt. Holyoke conference in harmonic analysis

arxiv created 2002/02/08 · arxiv updated 2009/11/30

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.

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• On the L^∞ norms of spectral projectors on shrinking intervals: the cases of some spheres of revolution and of the Euclidean disk

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