{
  "id": "0906.1374",
  "version": "v1",
  "published": "2009-06-07T18:28:27.000Z",
  "updated": "2009-06-07T18:28:27.000Z",
  "title": "Rapidly converging approximations and regularity theory",
  "authors": [
    "Shantanu Dave"
  ],
  "comment": "23 Pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\\Psi^{-\\infty}(M)\\to \\mathcal{C}^{\\infty}(M)$ are considered as generalized functions. For any collection of regularizing processes we produce an algebra of generalized functions and a diffeomorphism equivariant embedding of distributions into this algebra. We provide examples invariant under certain group actions. The regularity for such generalized functions is provided in terms of a certain tameness of maps between graded Frech\\'et spaces. This notion of regularity implies the regularity in Colombeau algebras in the $\\maG^{\\infty}$ sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-07T18:28:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rapidly converging approximations",
      "regularity theory",
      "generalized functions",
      "distributions",
      "closed compact manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1374D"
    }
  }
}