{
  "id": "math/0205094",
  "version": "v1",
  "published": "2002-05-09T11:38:13.000Z",
  "updated": "2002-05-09T11:38:13.000Z",
  "title": "Differential properties of matrix orthogonal polynomials",
  "authors": [
    "M. J. Cantero",
    "L. Moral",
    "L. Velazquez"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials. Several characterizations for these semi-classical functionals are given in terms of the corresponding (left) matrix orthogonal polynomials sequence. They involve a quasi-orthogonality property for their derivatives, a structure relation and a second order differo-differential equation. Finally we illustrate the preceding results with some non-trivial examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-09T11:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05"
    ],
    "keywords": [
      "differential properties",
      "second order differo-differential equation",
      "matrix orthogonal polynomials sequence",
      "semi-classical matrix orthogonal polynomials",
      "general theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5094C"
    }
  }
}