Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 257-268
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V. G. Doronin; A. A. Ligun. Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 257-268. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/
@article{MZM_1977_22_2_a9,
author = {V. G. Doronin and A. A. Ligun},
title = {Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of~$L$},
journal = {Matemati\v{c}eskie zametki},
pages = {257--268},
year = {1977},
volume = {22},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/}
}
TY - JOUR
AU - V. G. Doronin
AU - A. A. Ligun
TI - Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$
JO - Matematičeskie zametki
PY - 1977
SP - 257
EP - 268
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/
LA - ru
ID - MZM_1977_22_2_a9
ER -
%0 Journal Article
%A V. G. Doronin
%A A. A. Ligun
%T Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$
%J Matematičeskie zametki
%D 1977
%P 257-268
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/
%G ru
%F MZM_1977_22_2_a9
The lowest upper bound is obtained for best one-sided approximations of classes $W^rL_\psi$ ($r=1,2,\dots$) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space $L$, where $W^rL_\psi=\{f:f(x+2\pi)=f(x)$, $f^{(r-1)}(x)$ is absolutely continuous, $\|f^{(r)}\|_{L_\psi}\le1\}$ and $L_\psi$ is an Orlicz space.
