{
  "id": "1807.04347",
  "version": "v1",
  "published": "2018-07-11T20:38:40.000Z",
  "updated": "2018-07-11T20:38:40.000Z",
  "title": "Examples of de Branges-Rovnyak spaces generated by nonextreme functions",
  "authors": [
    "Bartosz Łanucha",
    "Maria T. Nowak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We describe de Branges-Rovnyak spaces $\\mathcal H (b_{\\alpha})$, $\\alpha>0$, where the function $b_{\\alpha}$ is not extreme in the unit ball of $H^{\\infty}$ on the unit disk $\\mathbb D$, defined by the equality $b_{\\alpha}(z)/a_{\\alpha}(z)=(1-z)^{-\\alpha}$, $z\\in\\mathbb D$, where $a_{\\alpha}$ is the outer function such that $a_{\\alpha}(0)>0$ and $|a_{\\alpha}|^2+|b_{\\alpha}|^2= 1$ a.e. on $\\partial \\mathbb D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-11T20:38:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B32",
      "30H10",
      "30H15"
    ],
    "keywords": [
      "branges-rovnyak spaces",
      "nonextreme functions",
      "unit disk",
      "outer function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}