{
  "id": "1104.4999",
  "version": "v2",
  "published": "2011-04-26T19:37:09.000Z",
  "updated": "2011-12-21T22:12:06.000Z",
  "title": "Szegő's theorem for matrix orthogonal polynomials",
  "authors": [
    "Maxim Derevyagin",
    "Olga Holtz",
    "Sergey Khrushchev",
    "Mikhail Tyaglov"
  ],
  "comment": "19 pp, typos corrected, introduction expanded",
  "journal": "Journal of Approximation Theory, 164/9 (2012), 1238-1261",
  "doi": "10.1016/j.jat.2012.05.003",
  "categories": [
    "math.CA",
    "math.CV",
    "math.PR",
    "math.RA"
  ],
  "abstract": "We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szeg\\H{o}'s theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-21T22:12:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "30C10",
      "62M10",
      "60G25",
      "46G10",
      "46G25",
      "15A54",
      "15A16",
      "15A45"
    ],
    "keywords": [
      "matrix orthogonal polynomials",
      "szegős theorem",
      "unit circle",
      "matrix case",
      "matrix analogue"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4999D"
    }
  }
}