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Approximation of holomorphic functions by Taylor-Abel-Poisson means

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Abstract

We investigate the problem of approximation of functions ƒ holomorphic in the unit disk by means A ρ, r (f) as ρ → 1−. In terms of the error of approximation by these means, a constructive characteristic of classes of holomorphic functions H p r Lipα is given. The problem of the saturation of A ρ, r (f) in the Hardy space H p is solved.

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Author information

Correspondence to V. V. Savchuk.

Additional information

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007.

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Savchuk, V.V. Approximation of holomorphic functions by Taylor-Abel-Poisson means. Ukr Math J 59, 1397–1407 (2007). https://doi.org/10.1007/s11253-007-0094-0

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Keywords

  • Holomorphic Function
  • Taylor Series
  • Hardy Space
  • Algebraic Polynomial
  • Taylor Formula