Fourier-Padé Approximants for Nikishin systems

  1. Lopez Lagomasino, G. 1
  2. Minguez Ceniceros, J. 2
  1. 1 Universidad Carlos III de Madrid
    info

    Universidad Carlos III de Madrid

    Madrid, España

    ROR https://ror.org/03ths8210

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Constructive Approximation

ISSN: 0176-4276

Any de publicació: 2008

Volum: 30

Número: 1

Pàgines: 53-69

Tipus: Article

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DOI: 10.1007/S00365-008-9023-1 SCOPUS: 2-s2.0-67650662451 WoS: WOS:000267104200004 GOOGLE SCHOLAR lock_opene-Archivo editor

Altres publicacions en: Constructive Approximation

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Ortogonalidad y aproximación: teoría y aplciaciones físicas y clínicas

2006/00095/001

Resum

We study type I Fourier-Padé approximation for certain systems of functions formed by the Cauchy transform of finite Borel measures supported on bounded intervals of the real line. This construction is similar to type I Hermite-Padé approximation. Instead of power series expansions of the functions in the system, we take their development in a series of orthogonal polynomials. We give the exact rate of convergence of the corresponding approximants. The answer is expressed in terms of the extremal solution of an associated vector-valued equilibrium problem for the logarithmic potential. © 2008 Springer Science+Business Media, LLC.