On n-Widths of a Sobolev Function Class in Orlicz Spaces

This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the e...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 31; no. 9; pp. 1475 - 1486
Main Authors Wang, Xiao Li, Wu, Ga Ridi
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.09.2015
Springer Nature B.V
Subjects
Approximation
Extreme values
Functional analysis
Functions (mathematics)
Kolmogorov宽度
Linear operators
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Optimization
Orlicz space
Orlicz空间
Sobolev函数类
Studies
Subspaces
度理论
极值问题
泛函分析
精确值
线性算子
width
41A46
Orlicz space
optimal linear operator
extremal subspace
41A30
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Summary:This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov＇s widths, Gelfand＇s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.
Bibliography:n-width, extremal subspace, optimal linear operator, Orlicz space
This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov＇s widths, Gelfand＇s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.
11-2039/O1
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4231-7