Completeness of boundary traces of eigenfunctions

@article{Han2015CompletenessOB,
  title={Completeness of boundary traces of eigenfunctions},
  author={XiaoLong Han and Andrew Hassell and Hamid Hezari and Steve Zelditch},
  journal={Proceedings of The London Mathematical Society},
  year={2015},
  volume={111},
  pages={749-773}
}
  • XiaoLong Han, Andrew Hassell, +1 author Steve Zelditch
  • Published 2015
  • Mathematics
  • Proceedings of The London Mathematical Society
  • 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.