On the equality of Kolmogorov and relative widths of classes of differentiable functions

被引：2

作者：

Subbotin, Yu. N. ^{[1
]}

Telyakovskii, S. A. ^{[2
]}

机构：

[1] Russian Acad Sci, Ural Div, Inst Math & Mech, Moscow 117901, Russia

[2] Russian Acad Sci, VA Steklov Math Inst, Moscow 117901, Russia

来源：

MATHEMATICAL NOTES | 2009年 / 86卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Kolmogorov width; relative width of a class; differentiable function; 2 pi-periodic function; Banach space; Favard constant;

D O I：

10.1134/S0001434609090168

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain sharper estimates of the remainders in the expression for the least value of the multiplier M for which the Kolmogorov widths d (n) (W (C) (r) , C) and the relative widths K (n) (W (C) (r) ,MW (C) (j) ,C) of the class W (C) (r) with respect to the class MW (C) (j) , j < r, where r - j is odd, are equal.

引用

页码：432 / 439

页数：8

共 50 条

[31] Kolmogorov and linear widths of weighted Besov classes
Dai, F
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 315 (02) : 711 - 724
[32] Kolmogorov widths of Sobolev classes on an irregular domain
O. V. Besov
Proceedings of the Steklov Institute of Mathematics, 2013, 280 : 34 - 45
[33] Kolmogorov widths of weighted Sobolev classes on a cube
Vasil'eva, A. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2010, 16 (04): : 100 - 116
[34] Kolmogorov Widths of Sobolev Classes on an Irregular Domain
Besov, O. V.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 280 (01) : 34 - 45
[35] Shape-preserving kolmogorov widths of classes of s-monotone integrable functions
V. N. Konovalov
Ukrainian Mathematical Journal, 2004, 56 (7) : 1074 - 1101
[36] Trigonometric Approximations and Kolmogorov Widths of Anisotropic Besov Classes of Periodic Functions of Several Variables
V. V. Myronyuk
Ukrainian Mathematical Journal, 2015, 66 : 1248 - 1266
[37] Shape-preserving Kolmogorov widths of classes of s-monotone integrable functions
Konovalov V.N.
Ukrainian Mathematical Journal, 2004, 56 (7) : 1074 - 1101
[38] Trigonometric Approximations and Kolmogorov Widths of Anisotropic Besov Classes of Periodic Functions of Several Variables
Myronyuk, V. V.
UKRAINIAN MATHEMATICAL JOURNAL, 2015, 66 (08) : 1248 - 1266
[39] Widths of classes of periodic differentiable functions in the space L2[0, 2π]
Shabozov, M. Sh.
MATHEMATICAL NOTES, 2010, 87 (3-4) : 575 - 581
[40] Widths of classes of periodic differentiable functions in the space L2[0, 2π]
M. Sh. Shabozov
Mathematical Notes, 2010, 87 : 575 - 581

← 1 2 3 4 5 →