{
  "id": "1706.01721",
  "version": "v1",
  "published": "2017-06-06T12:03:40.000Z",
  "updated": "2017-06-06T12:03:40.000Z",
  "title": "Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces",
  "authors": [
    "Aris Daniilidis",
    "Mounir Haddou",
    "Erwan Le Gruyer",
    "Olivier Ley"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\\frac{1+\\sqrt{3}}{2}$ in the sense of Le Gruyer [15].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-06T12:03:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert space",
      "glaeser-whitney extensions",
      "explicit formulas",
      "convex extension problem",
      "simple alternative proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}