Multiple orthogonal polynomials on the unit circle

  1. Ceniceros, J.M. 1
  2. Van Assche, W. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 KU Leuven
    info

    KU Leuven

    Lovaina, Bélgica

    ROR https://ror.org/05f950310

Journal:
Constructive Approximation

ISSN: 0176-4276

Year of publication: 2008

Volume: 28

Issue: 2

Pages: 173-197

Type: Article

DOI: 10.1007/S00365-007-0680-2 SCOPUS: 2-s2.0-38549102725 WoS: WOS:000251485100004 GOOGLE SCHOLAR

More publications in: Constructive Approximation

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Abstract

We introduce multiple orthogonal polynomials on the unit circle. We show how this is related to simultaneous rational approximation to Caratheodory functions (two-point Hermite-Pade approximation near zero and near infinity). We give a Riemann-Hilbert problem for which the solution is in terms of type I and type II multiple orthogonal polynomials on the unit circle, and recurrence relations are obtained from this Riemann-Hilbert problem. Some examples are given to give an idea of the behavior of the zeros of type II multiple orthogonal polynomials. © 2007 Springer.