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

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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Veröffentlicht in:Acta mathematica Sinica. English series 2015-09, Vol.31 (9), p.1475-1486
Hauptverfasser: Wang, Xiao Li, Wu, Ga Ridi
Format: Artikel
Sprache:eng
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4231-7