{
  "id": "0910.0155",
  "version": "v1",
  "published": "2009-10-01T12:25:30.000Z",
  "updated": "2009-10-01T12:25:30.000Z",
  "title": "Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators",
  "authors": [
    "Andreas Kriegl",
    "Peter W. Michor",
    "Armin Rainer"
  ],
  "comment": "8 pages",
  "journal": "Integral Equations and Operator Theory 71,3 (2011), 407-416",
  "doi": "10.1007/s00020-011-1900-5",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "Let $t\\mapsto A(t)$ for $t\\in T$ be a $C^M$-mapping with values unbounded operators with compact resolvents and common domain of definition which are self-adjoint or normal. Here $C^M$ stands for $C^\\om$ (real analytic), a quasianalytic or non-quasianalytic Denjoy-Carleman class, $C^\\infty$, or a H\\\"older continuity class $C^{0,\\al}$. The parameter domain $T$ is either $\\mathbb R$ or $\\mathbb R^n$ or an infinite dimensional convenient vector space. We prove and review results on $C^M$-dependence on $t$ of the eigenvalues and eigenvectors of $A(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-01T12:25:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C10",
      "26E10",
      "47A55"
    ],
    "keywords": [
      "denjoy-carleman differentiable perturbation",
      "unbounded operators",
      "infinite dimensional convenient vector space",
      "polynomials",
      "non-quasianalytic denjoy-carleman class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0155K"
    }
  }
}