Local and global analysis of eigenfunctions
Analysis of PDEs
2009-03-23 v1 Spectral Theory
Abstract
This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly compact and without boundary). We discuss both local results obtained by analyzing eigenfunctions on small balls, and global results obtained by wave equation methods. Among the main topics are nodal sets, quantum limits, and norms of global eigenfunctions.
Cite
@article{arxiv.0903.3420,
title = {Local and global analysis of eigenfunctions},
author = {Steve Zelditch},
journal= {arXiv preprint arXiv:0903.3420},
year = {2009}
}
Comments
A survey on eigenfunctions for the Handbook of Geometric Analysis, no. 1: L. Ji, P. Li, R. Schoen and L. Simon (eds.),