{
  "id": "1308.1061",
  "version": "v2",
  "published": "2013-08-05T18:36:35.000Z",
  "updated": "2014-05-04T07:44:41.000Z",
  "title": "Functional properties of Hörmander's space of distributions having a specified wavefront set",
  "authors": [
    "Yoann Dabrowski",
    "Christian Brouder"
  ],
  "comment": "38 pages, no figure. Nuclearity and further functional properties are added in this second version",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "The space $D'_\\Gamma$ of distributions having their wavefront sets in a closed cone $\\Gamma$ has become important in physics because of its role in the formulation of quantum field theory in curved space time. In this paper, the topological and bornological properties of $D'_\\Gamma$ and its dual $E'_\\Lambda$ are investigated. It is found that $D'_\\Gamma$ is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual $E'_\\Lambda$ is a nuclear, barrelled and bornological normal space of distributions which, however, is not even sequentially complete. Concrete rules are given to determine whether a distribution belongs to $D'_\\Gamma$, whether a sequence converges in $D'_\\Gamma$ and whether a set of distributions is bounded in $D'_\\Gamma$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-04T07:44:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "specified wavefront set",
      "distribution",
      "functional properties",
      "hörmanders space",
      "semi-montel complete normal space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-014-2156-0"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1246393,
      "adsabs": "2013arXiv1308.1061D"
    }
  }
}