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

ABDULLAYEV F., Savchuk V.

Journal of Mathematical Analysis and Applications, cilt.529, sa.2, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 529 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jmaa.2023.127298
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Blaschke product, Fejér type operator, Frostman condition, Holomorphic functions, Takenaka–Malmquist system
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.