Approximation by Fourier sums in classes of Weyl – Nagy differentiable functions with high exponent of smoothness

  • A. S. Serdyuk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev
  • I. V. Sokolenko Institute of Mathematics, National Academy of Sciences of Ukraine
Keywords: Fourier sum, Weyl-Nagy class, asymptotic equality

Abstract

UDC 517.5

We establish asymptotic estimates for the least upper bound of approximations in the uniform metric by Fourier sums of order $n-1$ in classes of $2\pi$-periodic Weyl-Nagy differentiable functions $W^r_{\beta,p},$ $1\le p\le \infty,$ $\beta\in\mathbb{R},$ with high exponents of smoothness $r\ (r-1\ge \sqrt{n}).$  We also obtain similar estimates for functional classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty.$

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Published
17.06.2022
How to Cite
Serdyuk, A. S., and I. V. Sokolenko. “Approximation by Fourier Sums in Classes of Weyl – Nagy Differentiable Functions With High Exponent of Smoothness”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 5, June 2022, pp. 685 -00, doi:10.37863/umzh.v74i5.7136.
Section
Research articles