{
  "id": "math-ph/0412054",
  "version": "v1",
  "published": "2004-12-16T16:08:38.000Z",
  "updated": "2004-12-16T16:08:38.000Z",
  "title": "Lieb-Thirring inequalities for higher order differential operators",
  "authors": [
    "Clemens Förster",
    "Jörgen Östensson"
  ],
  "comment": "18 pages, submitted to Comm. Part. Diff. Eq",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schr\\\"odinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators. For the critical case gamma = 1 - 1/2l in dimension d=1 with differential order 2l >= 4 we prove the strict inequality L^0(l,gamma,d) < L(l,gamma,d), which holds in contrast to current conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-16T16:08:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "47A75",
      "35J10"
    ],
    "keywords": [
      "higher order differential operators",
      "lieb-thirring inequalities",
      "differential order 2l",
      "strict inequality",
      "order gamma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.ph..12054F"
    }
  }
}