{
  "id": "1804.08512",
  "version": "v1",
  "published": "2018-04-23T15:37:48.000Z",
  "updated": "2018-04-23T15:37:48.000Z",
  "title": "The Bezout-corona problem revisited: Wiener space setting",
  "authors": [
    "G. J. Groenewald",
    "S. ter Horst",
    "M. A. Kaashoek"
  ],
  "comment": "21 pages",
  "journal": "Complex Analysis and Operator Theory 10 (2016), 115-139",
  "doi": "10.1007/s11785-015-0477-4",
  "categories": [
    "math.FA"
  ],
  "abstract": "The matrix-valued {Bezout-corona} problem $G(z)X(z)=I_m$, $|z|<1$, is studied in a Wiener space setting, that is, the given function $G$ is an analytic matrix function on the unit {disc} whose Taylor coefficients are absolutely summable and the same is required for the solutions $X$. It turns out that all Wiener solutions can be described explicitly in terms of two matrices and a square analytic Wiener function $Y$ satisfying $\\det Y(z)\\not =0$ for all $|z|\\leq 1$. It is also shown that some of the results hold in the $H^\\infty$ {setting, but} not all. In fact, if $G$ is an $H^\\infty$ function, then $Y$ is just an $H^2$ function. Nevertheless, in this case, using the two matrices and the function $Y$, all $H^2$ solutions to the Bezout-corona problem can be described explicitly in a form analogous to the one appearing in the Wiener setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T15:37:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A57",
      "47A53",
      "47B35",
      "46E40",
      "46E15"
    ],
    "keywords": [
      "wiener space setting",
      "bezout-corona problem",
      "square analytic wiener function",
      "analytic matrix function",
      "taylor coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}