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

Revue:
Constructive Approximation

ISSN: 0176-4276

Année de publication: 2008

Volumen: 28

Número: 2

Pages: 173-197

Type: Article

beta Ver similares en nube de resultados
DOI: 10.1007/S00365-007-0680-2 SCOPUS: 2-s2.0-38549102725 WoS: WOS:000251485100004 GOOGLE SCHOLAR

D'autres publications dans: Constructive Approximation

Dépôt institutionnel: lock_openAccès ouvert Editor

Objectifs de Développement Durable

Résumé

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.