{
  "id": "0902.1865",
  "version": "v1",
  "published": "2009-02-11T12:37:29.000Z",
  "updated": "2009-02-11T12:37:29.000Z",
  "title": "A global theory of algebras of generalized functions II: tensor distributions",
  "authors": [
    "Michael Grosser",
    "Michael Kunzinger",
    "Roland Steinbauer",
    "James Vickers"
  ],
  "comment": "Latex, 67 pages",
  "journal": "New York J. Math. 18 (2012) 139-199",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical embedding of distributional tensor fields also commutes with the Lie derivative. This construction provides the basis for applications of algebras of generalized functions in nonlinear distributional geometry and, in particular, to the study of spacetimes of low differentiability in general relativity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-11T12:37:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F30",
      "46T30",
      "26E15",
      "58B10",
      "46A17"
    ],
    "keywords": [
      "tensor distributions",
      "generalized functions",
      "global theory",
      "distributional tensor fields",
      "generalized tensor fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1865G"
    }
  }
}