{
  "id": "0812.2753",
  "version": "v2",
  "published": "2008-12-15T10:08:27.000Z",
  "updated": "2010-05-17T15:12:47.000Z",
  "title": "Note on the Fenchel transform in the Heisenberg group",
  "authors": [
    "A. Calogero",
    "R. Pini"
  ],
  "comment": "The paper appeared in Journal of Mathematical Analysis and Applications, volume 368, issue 1, August 2010, pages 69-79.",
  "categories": [
    "math.FA",
    "math.DG"
  ],
  "abstract": "Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the Euclidean case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-17T15:12:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A01",
      "53C17",
      "26B25"
    ],
    "keywords": [
      "heisenberg group",
      "abstract convexity",
      "crucial role",
      "main result",
      "euclidean case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2753C"
    }
  }
}