Norms of Modes and Quasi-modes revisited
John A. Toth, Steve Zelditch
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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