{
  "id": "1604.02846",
  "version": "v1",
  "published": "2016-04-11T09:05:53.000Z",
  "updated": "2016-04-11T09:05:53.000Z",
  "title": "The space $\\dot{\\mathcal{B}}'$ of distributions vanishing at infinity - duals of tensor products",
  "authors": [
    "Eduard A. Nigsch",
    "Norbert Ortner"
  ],
  "comment": "27 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Analogous to L.~Schwartz' study of the space $\\mathcal{D}'(\\mathcal{E})$ of semi-regular distributions we investigate the topological properties of the space $\\mathcal{D}'(\\dot{\\mathcal{B}})$ of semi-regular vanishing distributions and give representations of its dual and of the scalar product with this dual. In order to determine the dual of the space of semi-regular vanishing distributions we generalize and modify a result of A. Grothendieck on the duals of $E \\hat\\otimes F$ if $E$ and $F$ are quasi-complete and $F$ is not necessarily semi-reflexive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-11T09:05:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A32",
      "46F05"
    ],
    "keywords": [
      "tensor products",
      "distributions vanishing",
      "semi-regular vanishing distributions",
      "semi-regular distributions",
      "scalar product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160402846N"
    }
  }
}