{
  "id": "1311.0935",
  "version": "v3",
  "published": "2013-11-05T00:38:56.000Z",
  "updated": "2015-10-21T05:17:36.000Z",
  "title": "Completeness of boundary traces of eigenfunctions",
  "authors": [
    "Xiaolong Han",
    "Andrew Hassell",
    "Hamid Hezari",
    "Steve Zelditch"
  ],
  "comment": "This is the published version",
  "journal": "Proceeding of the London Mathematical Society (3) 111 (2015), no. 3, 749-773",
  "doi": "10.1112/plms/pdv018",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-02T22:57:57.000Z",
      "abstract": "Second version has generalised the theorems to smooth Riemannian manifolds with boundary, added the results of completeness of Cauchy data of eigenfunctions on interior submanifolds of arbitrary dimension, and provided an application to Kuznecov sum formulae. Several mistakes and typos have been corrected.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-21T05:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P10",
      "35P20",
      "35J05"
    ],
    "keywords": [
      "boundary traces",
      "completeness",
      "eigenfunctions",
      "kuznecov sum formulae",
      "smooth riemannian manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0935H"
    }
  }
}