Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 655-664
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N. P. Korneichuk. Best approximation by splines on classes of periodic functions in the metric of $L$. Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 655-664. http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a3/
@article{MZM_1976_20_5_a3,
author = {N. P. Korneichuk},
title = {Best approximation by splines on classes of periodic functions in the metric of $L$},
journal = {Matemati\v{c}eskie zametki},
pages = {655--664},
year = {1976},
volume = {20},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a3/}
}
TY - JOUR
AU - N. P. Korneichuk
TI - Best approximation by splines on classes of periodic functions in the metric of $L$
JO - Matematičeskie zametki
PY - 1976
SP - 655
EP - 664
VL - 20
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a3/
LA - ru
ID - MZM_1976_20_5_a3
ER -
%0 Journal Article
%A N. P. Korneichuk
%T Best approximation by splines on classes of periodic functions in the metric of $L$
%J Matematičeskie zametki
%D 1976
%P 655-664
%V 20
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a3/
%G ru
%F MZM_1976_20_5_a3
We have obtained the exact value of the upper bound on the best approximations in the metric of $L$ on the classes $W^rH^\omega$ of functions $f\in C_{2\pi}^r$ for which $|f^{(r)}(x')-f^{(r)}(x'')|\le\omega(|x'-x''|)$ [$\omega(t)$ is the upwards-convex modulus of continuity] by subspaces of $r$-th order polynomial splines of defect 1 with respect to the partitioning $k\pi/n$.
