On rational approximation and the discrete Hankel operator

• Vasiliy A. Prokhorov ^[1]
  1. [1] University of South Alabama

     University of South Alabama

     Estados Unidos

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 7, Nº. 1, 2015, págs. 123-136
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen
  • español

    Rational approximation, the AAK theorem, Hankel operator, singular value

  • English

    In this paper we investigate questions related to rational approximation of functions ʄ given on a finite set of points on the complex plane. We define the discrete Hankel operator Bf and investigate some of its properties. A theorem establishing a connection between the singular numbers of the discrete Hankel operator Bf and the errors in best rational approximation of ʄ is proved. This result is an analogue of the Adamyan-Arov-Krĕın theorem related to the theory of the Hardy spaces of analytic functions.