Application of the real Hardy – Sobolev space on the line to study the order of uniform rational approximations of functions

Authors

  • Tatsiana S. Mardvilko Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Aleksandr A. Pekarskii Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

Hardy space, Sobolev space, Hardy – Sobolev space, uniform rational approximations, even and odd continuations of functions
Supporting Agencies
The research was financially supported by the National Academy of Sciences of Belarus within the framework of the state program of scientific research «Convergence-2025».

Abstract

The real space of Hardy – Sobolev on a straight line is considered and some sufficient conditions for belonging to functions to this space are described. Estimates of the norm of functions from this space are also obtained. Various examples of functions from the Hardy – Sobolev space are given and the order of their best uniform rational approximations are investigated. Estimates of the best rational approximations for even and odd continuations of functions with monotonous derivatives are obtained. The order of the best rational approximations of the even and odd continuations of functions in the general case have also been studied. Estimates are given both considering the continuity module and without it. The obtained results are also used to study the best rational approximations of functions with a kink, introduced by A. A. Gonchar.

Author Biographies

  • Tatsiana S. Mardvilko, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); associate professor at the department of function theory, faculty of mechanics and mathematics

  • Aleksandr A. Pekarskii, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; professor at the department of function theory, faculty of mechanics and mathematics

References

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Published

2022-12-12

Issue

No. 3 (2022): Journal of the Belarusian State University. Mathematics and Informatics

Section

Real, Complex and Functional Analysis

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How to Cite

[1]
Mardvilko, T.S. and Pekarskii, A.A. 2022. Application of the real Hardy – Sobolev space on the line to study the order of uniform rational approximations of functions. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2022), 16–36. DOI:https://doi.org/10.33581/2520-6508-2022-3-16-36.