Asymptotics of approximation of conjugate functions by Poisson integrals

Yu. I. Kharkevych; K. V. Pozharska

doi:10.12697/ACUTM.2018.22.19

Yu. I. Kharkevych Faculty of Information Systems, Physics and Mathematics, Lesya Ukrainka Eastern European National University, 13 Volya Ave., Lutsk, 43025 Ukraine
K. V. Pozharska Institute of Mathematics of the National Academy of Sciences, 3 Tereschenkivska Str., Kiev, 01004 Ukraine

DOI: https://doi.org/10.12697/ACUTM.2018.22.19

Keywords: Poisson integral, asymptotic decomposition, Kolmogorov–Nikol'skii problem, conjugate function

Abstract

We obtain a decomposition of the upper bound for the deviation of Poisson integrals of conjugate periodic functions. The decomposition enables one to provide the Kolmogorov–Nikol'skii constants of an arbitrary order.

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