{
  "id": "1309.3449",
  "version": "v3",
  "published": "2013-09-13T13:38:01.000Z",
  "updated": "2014-12-16T12:11:45.000Z",
  "title": "Inverse problems and sharp eigenvalue asymptotics for Euler-Bernoulli operators",
  "authors": [
    "Andrey Badanin",
    "Evgeny Korotyaev"
  ],
  "comment": "33 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider Euler-Bernoulli operators with real coefficients on the unit interval. We prove the following results: i) Ambarzumyan type theorem about the inverse problems for the Euler-Bernoulli operator. ii) The sharp asymptotics of eigenvalues for the Euler-Bernoulli operator when its coefficients converge to the constant function. iii) The sharp eigenvalue asymptotics both for the Euler-Bernoulli operator and fourth order operators (with complex coefficients) on the unit interval at high energy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-16T16:34:41.000Z",
      "title": "Eigenvalue asymptotics for fourth order operators on the unit interval",
      "abstract": "We consider the fourth order operators $\\partial^4+2\\partial p\\partial +q$ with complex coefficients $p,q$ on the unit interval with the Dirichlet type boundary conditions. In the case of real coefficients our operator has a general form for the self-adjoint fourth order operator. We determine the sharp eigenvalue asymptotics at high energy: there are Fourier coefficients of both $p$ and $q$ in the main term.",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-16T12:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47E05",
      "34L20"
    ],
    "keywords": [
      "unit interval",
      "self-adjoint fourth order operator",
      "dirichlet type boundary conditions",
      "sharp eigenvalue asymptotics",
      "general form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3449B"
    }
  }
}