{
  "id": "math/9912216",
  "version": "v1",
  "published": "1999-12-28T15:12:54.000Z",
  "updated": "1999-12-28T15:12:54.000Z",
  "title": "A global theory of algebras of generalized functions",
  "authors": [
    "Michael Grosser",
    "Michael Kunzinger",
    "Roland Steinbauer",
    "James Vickers"
  ],
  "comment": "24 pages, LaTeX",
  "journal": "Advances in Math. 166 (2002) 50-72",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a geometric approach to defining an algebra $\\hat{\\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\\mathcal D}'(M)$ of distributions on $M$. Based on differential calculus in convenient vector spaces we achieve an intrinsic construction of $\\hat{\\mathcal G}(M)$. $\\hat{\\mathcal G}(M)$ is a{\\em differential} algebra, its elements possessing Lie derivatives with respect to arbitrary smooth vector fields. Moreover, we construct a canonical linear embedding of ${\\mathcal D}'(M)$ into $\\hat{\\mathcal G}(M)$ that renders ${\\mathcal C}^\\infty (M)$ a faithful subalgebra of $\\hat{\\mathcal G}(M)$. Finally, it is shown that this embedding commutes with Lie derivatives. Thus $\\hat{\\mathcal G}(M)$ retains all the distinguishing properties of the local theory in a global context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-28T15:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F30",
      "46T30"
    ],
    "keywords": [
      "generalized functions",
      "global theory",
      "arbitrary smooth vector fields",
      "convenient vector spaces",
      "elements possessing lie derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12216G"
    }
  }
}