On the best polynomial approximation in Hardy space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 110-123
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Sharp Jackson-Stechkin-type inequalities in which the best polynomial approximation of a function in the Hardy space $H_2$ is estimated from above both in terms of the generalized modulus of continuity of the $m$-th order and in terms of the $\mathcal{K}$-functional of $r$-th derivatives are found. For some classes of functions defined with the formulated characteristics in the space $H_2$, the exact values of $n$-widths are calculated. Also in the classes $W_{2}^{(r)}(\widetilde{\omega}_{m},\Phi)$ and $W_{2}^{(r)}(\mathcal{K}_{m},\Phi)$, where $r\in\mathbb{N}$, $r\ge2$ the exact values of the best polynomial approximations of intermediate derivatives $f^{(s)}$, $1\le s\le r-1$ are obtained.
Keywords:
the best polynomial approximation, generalized modulus of continuity, $\mathcal{K}$-functional, characteristic of smoothness, $n$-width.
@article{IVM_2022_11_a7,
author = {M. Sh. Shabozov and Z. Sh. Malakbozov},
title = {On the best polynomial approximation in {Hardy} space},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {110--123},
publisher = {mathdoc},
number = {11},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2022_11_a7/}
}
M. Sh. Shabozov; Z. Sh. Malakbozov. On the best polynomial approximation in Hardy space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 110-123. http://geodesic.mathdoc.fr/item/IVM_2022_11_a7/