Fejér-type positive operator based on Takenaka–Malmquist system on unit circle

ABDULLAYEV F., Savchuk V.

Journal of Mathematical Analysis and Applications, vol.529, no.2, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 529 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1016/j.jmaa.2023.127298
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Blaschke product, Fejér type operator, Frostman condition, Holomorphic functions, Takenaka–Malmquist system
  • Uşak University Affiliated: No

Abstract

Let φ={φk}k=−∞ ∞ denote the extended Takenaka–Malmquist system on unit circle T and let σn,φ(f), f∈L1(T), be the Fejér-type operator based on φ, introduced by V. N. Rusak. We give the convergence criteria for σn,φ(f) in Banach space C(T). Also we prove the Voronovskaya-type theorem for σn,φ(f) on class of holomorphic functions representable by Cauchy-type integrals with bounded densities.