{
  "id": "2203.08179",
  "version": "v1",
  "published": "2022-03-15T18:13:03.000Z",
  "updated": "2022-03-15T18:13:03.000Z",
  "title": "Free outer functions in complete Pick spaces",
  "authors": [
    "Alexandru Aleman",
    "Michael Hartz",
    "John E. McCarthy",
    "Stefan Richter"
  ],
  "comment": "63 pages",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function $f$ in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type $f=\\varphi g$, where $g$ is cyclic, $\\varphi$ is a contractive multiplier, and $\\|f\\|=\\|g\\|$. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-15T18:13:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "47A16",
      "47B32"
    ],
    "keywords": [
      "free outer functions",
      "complete pick spaces",
      "normalized complete pick reproducing kernel",
      "hilbert function space",
      "hardy space functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}