4 citations · 8 across the 9 of their papers we have counts for
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Estimates of deviations of Fourier sums on Weyl-Nagy classes
A. S. Serdyuk, I. V. Sokolenko
We establish estimates for exact upper bounds of deviations of partial Fourier sums on classes of -periodic functions whose $(r,β…
Approximation by Fourier sums on the classes of generalized Poisson integrals
Anatoly Serdyuk, Tetiana Stepaniuk
We present a survey of results related to the solution of Kolmogorov--Nikolsky problem for Fourier sums on the classes of generalized Poisson integrals , which consi…
Approximation by Fourier sums in classes of Weyl--Nagy differentiable functions with high exponent of smoothness
A. S. Serdyuk, I. V. Sokolenko
We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order of classes of -periodic Weyl--Nagy different…
About Lebesgue inequalities on the classes of generalized Poisson integrals
A. S. Serdyuk, T. A. Stepaniuk
For the functions , which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}π\int\limits_{-π}^π\sum\limits_{k=1}^{\infty}e^{-αk^{r}}\cos(kt-\frac{β…
Uniform approximations by Fourier sums on classes of convolutions of periodic functions
A. S. Serdyuk, T. A. Stepanyuk
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of -periodic functions, which are represented by convolutions…
Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals
Anatoly Serdyuk, Tetiana Stepaniuk
In this paper we establish Lebesgue-type inequalities for -periodic functions , which are defined by generalized Poisson integrals of the functions from , $1\leq…