{
  "id": "math/0606509",
  "version": "v1",
  "published": "2006-06-20T17:50:33.000Z",
  "updated": "2006-06-20T17:50:33.000Z",
  "title": "Spectral gap estimate for fractional Laplacian",
  "authors": [
    "M. Kwasnicki"
  ],
  "comment": "8 pages",
  "journal": "Probab. Math. Statist. 28(1) (2008) 163-167",
  "categories": [
    "math.PR"
  ],
  "abstract": "A lower bound estimate \\lambda_2 - \\lambda_1 \\ge c \\lambda_1^{-d / \\alpha} (\\diam D)^{-d - \\alpha} for the spectral gap of the Dirichlet fractional Laplacian on arbitrary bounded domain D is proved. This follows from a variational formula for the spectral gap and an upper bound estimate for the supremum norm of the ground state eigenfunction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-20T17:50:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral gap estimate",
      "lower bound estimate",
      "ground state eigenfunction",
      "dirichlet fractional laplacian",
      "upper bound estimate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6509K"
    }
  }
}