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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
G. Hardy and J. E. Littlewood, “Some properties of fractional integrals. II,” Math. Z., 34, 403–439 (1931).
P. Duren, Theory of H p Spaces, Academic Press, New York (1970).
V. T. Gavrilyuk and A. I. Stepanets, “Problems of saturation of linear methods,” Ukr. Mat. Zh., 43, No. 3, 291–308 (1991).
A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, (2002).
P. Butzer and J. R. Nessel, Fourier Analysis and Approximation, Birkhäuser, Basel (1971).
A. Zygmund, “Smooth functions,” Duke Math. J., 12, 47–76 (1945).
A. Zygmund, Trigonometric Series [Russian translation], Vol. 1, Mir, Moscow (1965).
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007.
About this article
Cite this article
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
- Holomorphic Function
- Taylor Series
- Hardy Space
- Algebraic Polynomial
- Taylor Formula