{
  "id": "1005.0833",
  "version": "v3",
  "published": "2010-05-05T19:48:24.000Z",
  "updated": "2013-03-06T09:32:04.000Z",
  "title": "Phase-space analysis and pseudodifferential calculus on the Heisenberg group",
  "authors": [
    "Hajer Bahouri",
    "Clotilde Fermanian-Kammerer",
    "Isabelle Gallagher"
  ],
  "comment": "The definition of symbols has been made precise by specifying the regularity needed need $\\lambda = 0$",
  "categories": [
    "math.AP"
  ],
  "abstract": "A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on Sobolev spaces and the loss of derivatives may be controled by the order of the operator. Although a large number of works have been devoted in the past to the construction and the study of algebras of variable-coefficient operators, including some very interesting works on the Heisenberg group, our approach is different, and in particular puts into light microlocal directions and completes, with the Littlewood-Paley theory developed in \\cite{bgx} and \\cite{bg}, a microlocal analysis of the Heisenberg group.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-06T09:32:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg group",
      "pseudodifferential calculus",
      "phase-space analysis",
      "light microlocal directions",
      "microlocal analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.0833B"
    }
  }
}