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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Dynamical Systems
Volume 10 - 2024 | doi: 10.3389/fams.2024.1437247
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 13 articles

Approximation of classes of Poisson integrals by rectangular Fej ér means

Provisionally accepted
Olga Rovenska Olga Rovenska *
  • Institute of Mathematics (NAN Ukraine), Kyiv, Ukraine

The final, formatted version of the article will be published soon.

    The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fej ér means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression.In one-dimensional case, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of complex plane.

    Keywords: linear method of approximation, extremal problem of approximation theory, Poisson integral, Fej ér mean, exact asymptotic

    Received: 23 May 2024; Accepted: 10 Jul 2024.

    Copyright: © 2024 Rovenska. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Olga Rovenska, Institute of Mathematics (NAN Ukraine), Kyiv, Ukraine

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