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arXiv · 1311.0935

Completeness of boundary traces of eigenfunctions

Xiaolong Han·Andrew Hassell·Hamid Hezari·Steve Zelditch
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Abstract

In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by Bäcker, Fürstburger, 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.

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Xiaolong Han, Andrew Hassell, Hamid Hezari, Steve Zelditch. 2015-10-21. Completeness of boundary traces of eigenfunctions. https://doi.org/10.1112/plms%2Fpdv018

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