{
  "id": "0808.0382",
  "version": "v1",
  "published": "2008-08-04T06:37:43.000Z",
  "updated": "2008-08-04T06:37:43.000Z",
  "title": "Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients",
  "authors": [
    "Maxim Zinchenko"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Vel\\'azquez) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result on CMV operators with scalar-valued coefficients. In the course of deriving the Borg-type result we also use exponential Herglotz representations of Caratheodory matrix-valued functions to prove an infinite sequence of trace formulas connected with CMV operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-04T06:37:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B36",
      "34A55",
      "47A10"
    ],
    "keywords": [
      "trace formulas",
      "borg-type theorem",
      "matrix-valued coefficients",
      "general borg-type inverse spectral result",
      "verblunsky coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.0382Z"
    }
  }
}