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...
Saved in:
Published in | Acta mathematica Sinica. English series Vol. 31; no. 9; pp. 1475 - 1486 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Beijing
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.09.2015
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 ObjectType-Feature-2 content type line 23 |
ISSN: | 1439-8516 1439-7617 |
DOI: | 10.1007/s10114-015-4231-7 |