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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 538–551
DOI: https://doi.org/10.4213/mzm4617
(Mi mzm4617)
 

This article is cited in 5 scientific papers (total in 5 papers)

Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2

V. F. Babenkoab, N. V. Parfinovichb

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Dnepropetrovsk National University
Full-text PDF (569 kB) Citations (5)
References:
Abstract: 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.
Received: 07.03.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 515–527
DOI: https://doi.org/10.1134/S0001434609030237
Bibliographic databases:
UDC: 517
Language: Russian
Citation: V. F. Babenko, N. V. Parfinovich, “Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2”, Mat. Zametki, 85:4 (2009), 538–551; Math. Notes, 85:4 (2009), 515–527
Citation in format AMSBIB
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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