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Publications Influence

Estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics

- T. Stepaniuk
- Mathematics
- 22 April 2014

In metric of spaces $L_{s}, \ 1< s\leq\infty$, we obtain exact order estimates of best approximations and approximations by Fourier sums of classes of convolutions the periodic functions that belong… Expand

3 1- PDF

Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 27 April 2013

We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2\pi$-periodic continuous functions, which… Expand

1 1- PDF

Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 16 April 2018

For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms… Expand

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About Lebesgue inequalities on the classes of generalized Poisson integrals

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 28 May 2020

For the functions $f$, which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}{\pi}\int\limits_{-\pi}^{\pi}\sum\limits_{k=1}^{\infty}e^{-\alpha… Expand

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 26 August 2019

In this paper we establish Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $\varphi$ from $L_{p}$, $1\leq p< \infty$.… Expand

Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 14 October 2014

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq… Expand

Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction

- Adrian Ebert, P. Kritzer, O. Osisiogu, T. Stepaniuk
- Computer Science, Mathematics
- ArXiv
- 29 January 2021

TLDR

Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (\psi, \beta)-differentiable functions

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 10 October 2015

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of… Expand

Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces

- Adrian Ebert, P. Kritzer, O. Osisiogu, T. Stepaniuk
- Mathematics, Computer Science
- ArXiv
- 20 August 2020

TLDR

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

- A. Serdyuk, T. Stepaniuk
- Mathematics
- 14 October 2014

In metric of spaces $L_{s}, \ 1\leq s\leq\infty$, we obtain exact in order estimates of best $m$-term trigonometric approximations of classes of convolutions of periodic functions, that belong to… Expand

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