Completeness of boundary traces of eigenfunctions
Analysis of PDEs
2015-10-22 v3 Spectral Theory
Abstract
In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by B\"acker, F\"urstburger, Schubert, and Steiner, expressing (in some sense) the asymptotic completeness of the set of boundary traces in a frequency window of size O(1), is proved both for Dirichlet and Neumann boundary conditions. We then prove a semiclassical generalization of this identity.
Cite
@article{arxiv.1311.0935,
title = {Completeness of boundary traces of eigenfunctions},
author = {Xiaolong Han and Andrew Hassell and Hamid Hezari and Steve Zelditch},
journal= {arXiv preprint arXiv:1311.0935},
year = {2015}
}
Comments
This is the published version