Resumen de On rational approximation and the discrete Hankel operator

V. A. Prokhorov

• 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.