{
  "id": "math/0204294",
  "version": "v1",
  "published": "2002-04-24T13:52:00.000Z",
  "updated": "2002-04-24T13:52:00.000Z",
  "title": "A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line",
  "authors": [
    "Maria J. Cantero",
    "Maria P. Ferrer",
    "Leandro Moral",
    "Luis Velazquez"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials L, and leads to a new orthogonality structure in the module LxL. This structure can be interpreted in terms of a 2x2 matrix measure on [-1,1], and semi-orthogonal functions provide the corresponding sequence of orthogonal matrix polynomials. This gives a connection between orthogonal polynomials on the unit circle and certain classes of matrix orthogonal polynomials on [-1,1]. As an application, the strong asymptotics of these matrix orthogonal polynomials is derived, obtaining an explicit expression for the corresponding Szego's matrix function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-24T13:52:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05"
    ],
    "keywords": [
      "matrix orthogonal polynomials",
      "unit circle",
      "real line",
      "connection",
      "semi-orthogonal functions"
    ],
    "publication": {
      "doi": "10.1016/S0377-0427(02)00824-5",
      "journal": "Journal of Computational and Applied Mathematics",
      "year": 2003,
      "month": "May",
      "volume": 154,
      "number": 2,
      "pages": 247
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JCoAM.154..247C"
    }
  }
}