Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Serdyuk, A. S."'
Autor:
Serdyuk, A. S., Stepaniuk, T. A.
We establish interpolation analogues of Lebesgue type inequalities on the sets of $C^{\psi}_{\beta}L_{1}$ $2\pi$-periodic functions $f$, which are representable as convolutions of generating kernel $\Psi_{\beta}(t) = \sum\limits_{k=1}^{\infty}\psi(k)
Externí odkaz:
http://arxiv.org/abs/2308.12184
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such that $\|\varphi\|_2\le1$, with fixed generated kernels $\Psi_{\bar{\beta}}$, which have Fo
Externí odkaz:
http://arxiv.org/abs/2304.04586
Autor:
Serdyuk, A. S., Sokolenko, I. V.
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 $2\pi$-periodic Weyl--Nagy differentiable functions, $W^r_{\beta,p}, 1\le p\le \infty, \beta\in\mathbb{R
Externí odkaz:
http://arxiv.org/abs/2202.03113
This review paper presents the results, which cover the study of current problems of approximation theory in abstract linear spaces. Such research has been actively developed since the 2000s, based on the ideas and approaches initiated in the article
Externí odkaz:
http://arxiv.org/abs/2104.04252
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We find two-sides estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels, modules of Fourier coefficients of which satisfy the condi
Externí odkaz:
http://arxiv.org/abs/2008.01450
Autor:
Serdyuk, A. S., Stepaniuk, T. A.
For the functions $f$, which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}{\pi}\int\limits_{-\pi}^{\pi}\sum\limits_{k=1}^{\infty}e^{-\alpha k^{r}}\cos(kt-\frac{\beta\pi}{2})\varphi(x-t)dt$, $\varphi\perp1$, $\alpha>
Externí odkaz:
http://arxiv.org/abs/2005.13849
Autor:
Serdyuk, A. S., Stepanyuk, T. A.
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2\pi$-periodic functions, which are represented by convolutions of functions $\varphi (\varphi\bot 1)$ from unit ball of the space $
Externí odkaz:
http://arxiv.org/abs/2001.00374
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\beta,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform metric. We obtai
Externí odkaz:
http://arxiv.org/abs/1906.02531
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with the equidistant nodes $x_k^{(n-1)}=\frac{2k\pi}{2n-1},\ k\in\mathbb{Z},$ in metrics of the spaces $L_p$ on classes of $2\
Externí odkaz:
http://arxiv.org/abs/1806.02561
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the space $L_2$,
Externí odkaz:
http://arxiv.org/abs/1703.09048