Estimates of the best m-term trigonometric approximations of classes of analytic functions

Authors

  • А. S. Serdyuk
  • Т.А. Stepanyuk

DOI:

https://doi.org/10.15407/dopovidi2015.02.032

Keywords:

analytic function, trigonometric approximation

Abstract

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References

Stepanets A. I. Methods of Approximation Theory. Pt. I, Kyiv, 2002 (Pratsi Inst. matematyky NAN Ukr., Vol. 40) (in Russian).

Stepanets A. Y., Serdiuk A. S., Shidlich A. L. Ukr. mat. zhurn., 2008, 60, No 12: 1686–1708 (in Russian).

Stechkin S. B. Dokl. AN SSSR, 1955, 102, No 1: 37–40 (in Russian).

Fedorenko O. S. Approaching (ψ; β) - differentiable functions by trigonometric polynomials: Avtoref. dis. kand. fiz.-mat. sci. Institute of mathematics NAS of Ukrainy, Kyiv, Ukraine, 2001 (in Ukrainian).

Fedorenko A. S., Fedorenko O. S. Best m-membered tryhonometrychni approximation classes Lψβ, p in the uniform metric. In: Proceedings of the Institute for Mathematics NAS Ukraine, Vol. 46, (pp. 276–282), Kyiv, 2003 (in Ukrainian).

Fedorenko A. S., Fedorenko O. S. Ukr. mat. zhurn., 2004, 56, No 1: 129–132 (in Ukrainian).

Romanyuk A. S. Izv. RAN. Ser. mat., 2003, 67, No 2: 61–100 (in Russian).

Romanyuk A. S. Mat. zametki, 2007, 81, No 2: 247–261 (in Russian).

Romanyuk A. S. Approximation characteristics of the classes of Periodic Functions of many variables. In: Proceedings of the Institute for Mathematics NAS Ukraine, Vol. 93, Kyiv, 2012: (in Russian).

Stepanets A. I. Methods of Approximation Theory. Pt. II. In: Proceedings of the Institute for Mathematics NAS Ukraine, Vol. 40, Kyiv, 2002 (in Russian).

Romanyuk V. S. Additions to the approximation by Fourier sums estimated classes of infinitely differentiable functions. In: Proceedings of the Institute for Mathematics NAS Ukraine, Vol. 46, (pp. 131–135), Kyiv, 2003 (in Russian).

Grabova U. Z., Serdiuk A. S. Ukr. mat. zhurn., 2013, 65, No 9: 1186–1197 (in Ukrainian); English translation: Hrabova, U.Z. & Serdyuk, A.S. Ukr Math J (2014) 65: 1319. DOI: https://doi.org/10.1007/s11253-014-0861-7

Korneichuk N. P. Exact constants in approximation theory, Moscow: Nauka, 1987 (in Russian).

Serdyuk A.S., Stepanyuk T.A. Ukr. mat. zhurn. 2014, 66, No 9:1244–1256 (in Ukrainian); English translation: Serdyuk, A.S. & Stepanyuk, T.A. Ukr Math J (2015) 66: 1862. DOI: https://doi.org/10.1007/s11253-015-1056-6

Published

08.01.2025

How to Cite

Serdyuk А. S., & Stepanyuk Т. (2025). Estimates of the best m-term trigonometric approximations of classes of analytic functions . Reports of the National Academy of Sciences of Ukraine, (2), 32–37. https://doi.org/10.15407/dopovidi2015.02.032