Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 538-551
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We obtain exact values of best $L_1$-approximations for the classes $W^rF$, $r\in\mathbb N$, of periodic functions whose $r$th derivative belongs to a given rearrangement-invariant set $F$ as well as for the classes $W^rH^\omega$ of periodic functions whose $r$th derivative has a given convex (up) majorant $\omega(t)$ of the modulus of continuity by subspaces of polynomial splines of order $m\ge r+1$ of deficiency 2 with nodes at the points $2k\pi/n$, $n\in\mathbb N$, $k\in\mathbb Z$. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding function classes.
Keywords:
periodic function, best $L_1$-approximation, periodic function, polynomial spline of deficiency 2, Kolmogorov width, rearrangement-invariant set, modulus of continuity.
@article{MZM_2009_85_4_a4,
author = {V. F. Babenko and N. V. Parfinovich},
title = {Exact {Values} of {Best} {Approximations} for {Classes} of {Periodic} {Functions} by {Splines} of {Deficiency~2}},
journal = {Matemati\v{c}eskie zametki},
pages = {538--551},
publisher = {mathdoc},
volume = {85},
number = {4},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a4/}
}
TY - JOUR AU - V. F. Babenko AU - N. V. Parfinovich TI - Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2 JO - Matematičeskie zametki PY - 2009 SP - 538 EP - 551 VL - 85 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a4/ LA - ru ID - MZM_2009_85_4_a4 ER -
%0 Journal Article %A V. F. Babenko %A N. V. Parfinovich %T Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2 %J Matematičeskie zametki %D 2009 %P 538-551 %V 85 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a4/ %G ru %F MZM_2009_85_4_a4
V. F. Babenko; N. V. Parfinovich. Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 538-551. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a4/