Inspé - Accueil

Lower bounds in $H^2$-rational approximation to Blaschke products

AUTHORS

  • Baratchart Laurent
  • Borichev Alexander
  • Chevillard Sylvain
  • Coiffard Marre Claire
  • Zarouf Rachid

KEYWORDS

  • Blaschke product
  • Hardy space H2
  • Lower bounds
  • Complex rational approximation

    • Document type

    Journal articles

    Abstract

    We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space $H^2$ of the unit disk. We first consider approximation to $z^N$, and then move on to more general Blaschke products whose zeros are bounded away from the circle. The latter case depends on Fourier coefficients estimates for Blaschke products which are of independent interest.

    FILE

    MORE INFORMATION