{
  "id": "1909.03662",
  "version": "v1",
  "published": "2019-09-09T07:08:16.000Z",
  "updated": "2019-09-09T07:08:16.000Z",
  "title": "Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects",
  "authors": [
    "Paul Alphonse",
    "Joackim Bernier"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study semigroups generated by accretive non-selfadjoint quadratic differential operators. We give a description of the polar decomposition of the associated evolution operators as products of a selfadjoint operator and a unitary operator. The selfadjoint parts turn out to be also evolution operators generated by time-dependent real-valued quadratic forms that are studied in details. As a byproduct of this decomposition, we give a geometric description of the regularizing properties of semigroups generated by accretive non-selfadjoint quadratic operators. Finally, by using the interpolation theory, we take advantage of this smoothing effect to establish subelliptic estimates enjoyed by quadratic operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-09T07:08:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polar decomposition",
      "regularizing effects",
      "semigroups",
      "accretive non-selfadjoint quadratic differential operators",
      "evolution operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}