Xiaolong Han, Andrew Hassell, Hamid Hezari, Steve Zelditch
Published 2013-11-05, updated 2015-10-21Version 3
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.
Comments: This is the published version
Journal: Proceeding of the London Mathematical Society (3) 111 (2015), no. 3, 749-773
Billiards and boundary traces of eigenfunctions
Completeness of the set $\{e^{ikβ\cdot s}\}|_{\forall β\in S^2}$
$L^p$ bounds on eigenfunctions for operators with double characteristics
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