I. V. Sokolenko

activity

20132025

most citedApproximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

4 citations · 6 across the 8 of their papers we have counts for

collaborators

8 papers

math.CA2025

Estimates of deviations of Fourier sums on Weyl-Nagy classes $W_{β, 1}^{r}$

A. S. Serdyuk, I. V. Sokolenko

We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n - 1} (f)$ on classes $W_{β, 1}^{r}, r > 2, β \in R,$ of $2 π$ -periodic functions whose $(r,β…

math.CA2023

Asymptotic estimates for the widths of classes of functions of high smoothness

A. S. Serdyuk, I. V. Sokolenko

We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2 π$ -periodic functions $φ$ , such that $∥ φ ∥_{2} \leq 1$ , with fix…

math.CA2022

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 $n - 1$ of classes of $2 π$ -periodic Weyl--Nagy different…

math.CA2020

Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

A. S. Serdyuk, I. V. Sokolenko

We find two-sides estimates for the best uniform approximations of classes of convolutions of $2 π$ -periodic functions from unit ball of the space $L_{p}, 1 \leq p < \infty,$ with fixed…

math.CA2019★ 4 cited

Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

A. S. Serdyuk, I. V. Sokolenko

We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W_{β, p}^{r}, 1 \leq p \leq \infty,$ for rapidly growing exponents of smoot…

math.CA2018

Approximation by interpolation trigonometric polynomials in metrics of the spaces $L_{p}$ on the classes of periodic entire functions

A. S. Serdyuk, I. V. Sokolenko

We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with the equidistant nodes $x_k^{(n-1)}=\frac{2kπ}{2n-1}…

math.CA2017★ 2 cited

Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients

A. S. Serdyuk, I. V. Sokolenko

We calculate the least upper bounds of pointwise and uniform approximations for classes of $2 π$ -periodic functions expressible as convolutions of an arbitrary square summable kerne…

math.CA2013

Approximation by linear methods of classes of $(ψ, β ˉ) -$ differentiable functions

A. S. Serdyuk, I. V. Sokolenko

We calculate the least upper bounds for approximations in the metric of the space $L_{2}$ by linear methods of summation of Fourier series on classes of periodic functions $L^ψ_{\bar…

Estimates of deviations of Fourier sums on Weyl-Nagy classes Wβ,1r​

Asymptotic estimates for the widths of classes of functions of high smoothness

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

Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

Approximation by interpolation trigonometric polynomials in metrics of the spaces Lp​ on the classes of periodic entire functions

Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients

Approximation by linear methods of classes of (ψ,βˉ​)−differentiable functions

Estimates of deviations of Fourier sums on Weyl-Nagy classes $W_{β, 1}^{r}$

Approximation by interpolation trigonometric polynomials in metrics of the spaces $L_{p}$ on the classes of periodic entire functions

Approximation by linear methods of classes of $(ψ, β ˉ) -$ differentiable functions