{
  "id": "1008.2099",
  "version": "v2",
  "published": "2010-08-12T11:35:53.000Z",
  "updated": "2011-03-15T15:48:56.000Z",
  "title": "Persistence of embedded eigenvalues",
  "authors": [
    "Shmuel Agmon",
    "Ira Herbst",
    "Sara Maad Sasane"
  ],
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < \\infty we show that in favorable situations the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of co-dimension m.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-15T15:48:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q15"
    ],
    "keywords": [
      "embedded eigenvalue",
      "small perturbations",
      "persistence",
      "simple eigenvalue",
      "self-adjoint operator remains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2099A"
    }
  }
}