{
  "id": "1804.08518",
  "version": "v1",
  "published": "2018-04-23T15:44:47.000Z",
  "updated": "2018-04-23T15:44:47.000Z",
  "title": "The Bezout equation on the right half plane in a Wiener space setting",
  "authors": [
    "G. J. Groenewald",
    "S. ter Horst",
    "M. A. Kaashoek"
  ],
  "comment": "15 pages",
  "journal": "Operator Theory: Advances and Applications 259 (2017), 395-411",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper deals with the Bezout equation $G(s)X(s)=I_m$, $\\Re s \\geq 0$, in the Wiener space of analytic matrix-valued functions on the right half plane. In particular, $G$ is an $m\\times p$ matrix-valued analytic Wiener function, where $p\\geq m$, and the solution $X$ is required to be an analytic Wiener function of size $p\\times m$. The set of all solutions is described explicitly in terms of a $p\\times p$ matrix-valued analytic Wiener function $Y$, which has an inverse in the analytic Wiener space, and an associated inner function $\\Theta$ defined by $Y$ and the value of $G$ at infinity. Among the solutions, one is identified that minimizes the $H^2$-norm. A Wiener space version of Tolokonnikov's lemma plays an important role in the proofs. The results presented are natural analogs of those obtained for the discrete case in [11].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T15:44:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A56",
      "47A57",
      "47B35",
      "46E40",
      "46E15"
    ],
    "keywords": [
      "right half plane",
      "wiener space setting",
      "bezout equation",
      "matrix-valued analytic wiener function",
      "wiener space version"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}