{
  "id": "math/0101224",
  "version": "v1",
  "published": "2001-01-26T22:03:51.000Z",
  "updated": "2001-01-26T22:03:51.000Z",
  "title": "Unitary interpolants and factorization indices of matrix functions",
  "authors": [
    "R. B. Alexeev",
    "V. V. Peller"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "For an $n\\times n$ bounded matrix function $\\Phi$ we study unitary interpolants $U$, i.e., unitary-valued functions $U$ such that $\\hat U(j)=\\hat\\Phi(j)$, $j<0$. We are looking for unitary interpolants $U$ for which the Toeplitz operator $T_U$ is Fredholm. We give a new approach based on superoptimal singular values and thematic factorizations. We describe Wiener--Hopf factorization indices of $U$ in terms of superoptimal singular values of $\\Phi$ and thematic indices of $\\Phi-F$, where $F$ is a superoptimal approximation of $\\Phi$ by bounded analytic matrix functions. The approach essentially relies on the notion of a monotone thematic factorization introduced in [AP]. In the last section we discuss hereditary properties of unitary interpolants. In particular, for matrix functions $\\Phi$ of class $H^\\be+C$ we study unitary interpolants $U$ of class $QC$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-26T22:03:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "46E15",
      "30D55"
    ],
    "keywords": [
      "study unitary interpolants",
      "superoptimal singular values",
      "monotone thematic factorization",
      "wiener-hopf factorization indices",
      "bounded analytic matrix functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......1224A"
    }
  }
}