Completeness of boundary traces of eigenfunctions

Xiaolong Han, Andrew Hassell, Hamid Hezari, Steve Zelditch

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 ['Behaviour of boundary functions for quantum billiards', J. Phys. A 35 (2002) 10293-10310], 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.

Original languageEnglish (US)
Pages (from-to)749-773
Number of pages25
JournalProceedings of the London Mathematical Society
Issue number3
StatePublished - May 29 2014

ASJC Scopus subject areas

  • General Mathematics


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