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of 37
pro vyhledávání: '"Sokolenko, I. V."'
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
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., 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
Autor:
Serdyuk, A. S., Sokolenko, I. V.
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 $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and sh
Externí odkaz:
http://arxiv.org/abs/1303.1300
Autor:
Serdyuk, A. S., Sokolenko, I. V.
We obtain asymptotic estimates for the best approximations by trigonometric polynomials in the metric space $C$ $(L_p)$ of classes of periodic functions that can be represented as a convolution of kernels $\Psi_\beta$, which Fourier coefficients tend
Externí odkaz:
http://arxiv.org/abs/1212.2096
Autor:
Serdyuk, A. S.1 (AUTHOR), Sokolenko, I. V.1 (AUTHOR) sokol@imath.kiev.ua
Publikováno v:
Ukrainian Mathematical Journal. Oct2022, Vol. 74 Issue 5, p783-800. 18p.
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