Abstract
The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis of the Faber polynomials after the summation of Faber series. Analogs of the author's results are obtained for the classesL Ψβ
in the periodic case.
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V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).
V. I. Smirnov and N. A. Lebedev,The Constructive Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1964).
P. K. Suetin,Series in the Faber Polynomials [in Russian], Nauka, Moscow (1984).
P. M. Tamrazov,Smoothness and Polynomial Approximations [in Russian], Naukova Dumka, Kiev (1975).
A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
A. I. Stepanets, “On the Lebesgue inequality on the classes of (ψ, β)-differentiable functions,”Ukr. Mat. Zh.,41, No. 5, 499–510 (1989).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. I,”Ukr. Mat. Zh.,42, No. 1, 102–112 (1990).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. II,”Ukr. Mat. Zh.,42, No. 2, 210–222 (1990).
A. Zygmund,Trigonometric Series, Vol. 2, Cambridge University Press, Cambridge (1959).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 809–833, June, 1993.
This paper was supported by the Ukrainian State Committee for Science and Technology.
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Stepanets, A.I. Approximation of cauchy-type integrals in Jordan domains. Ukr Math J 45, 890–917 (1993). https://doi.org/10.1007/BF01061441
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DOI: https://doi.org/10.1007/BF01061441