{
  "id": "1212.0235",
  "version": "v1",
  "published": "2012-12-02T19:25:08.000Z",
  "updated": "2012-12-02T19:25:08.000Z",
  "title": "On the measure of the spectrum of direct integrals",
  "authors": [
    "Anton A. Kutsenko"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "We obtain the estimate of the Lebesgue measure of the spectrum for the direct integral of matrix-valued functions. These estimates are applicable for a wide class of discrete periodic operators. For example: these results give new and sharp spectral bounds for 1D periodic Jacobi matrices and 2D discrete periodic Schrodinger operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-02T19:25:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct integral",
      "2d discrete periodic schrodinger operators",
      "1d periodic jacobi matrices",
      "discrete periodic operators",
      "sharp spectral bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0235K"
    }
  }
}