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 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Wang, Xiao Li Wu, Ga Ridi |
| description | 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. |
| doi_str_mv | 10.1007/s10114-015-4231-7 |
| format | Article |
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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.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-015-4231-7</identifier><language>eng</language><publisher>Beijing: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</publisher><subject>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</subject><ispartof>Acta mathematica Sinica. 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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.</description><subject>Approximation</subject><subject>Extreme values</subject><subject>Functional analysis</subject><subject>Functions (mathematics)</subject><subject>Kolmogorov宽度</subject><subject>Linear operators</subject><subject>Mathematical analysis</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization</subject><subject>Orlicz space</subject><subject>Orlicz空间</subject><subject>Sobolev函数类</subject><subject>Studies</subject><subject>Subspaces</subject><subject>度理论</subject><subject>极值问题</subject><subject>泛函分析</subject><subject>精确值</subject><subject>线性算子</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kDFPwzAQhS0EEqXwA9gsWFgMPjuO4xFVFJCQOhTEaDmO26ZK7TZOkODX4yoVQgxMd8P33rt7CF0CvQVK5V0ECpARCoJkjAORR2gEGVdE5iCPD3shID9FZzGuKRVC0XyEipnHnrzXVbeKOCywwfNQhsZ94GnvbVcHjyeNiRHXHs_aprZfeL411sVzdLIwTXQXhzlGb9OH18kTeZk9Pk_uX4jlrOiILCVfAGNcCQOWOyGMstwCVZmqrJUGVKUss05KWRgLVWlLR40pnWFlaSkfo5vBd9uGXe9ipzd1tK5pjHehjxokT59DTkVCr_-g69C3Pl2XKAoFK1SRJwoGyrYhxtYt9LatN6b91ED1vks9dKlTl3rfpZZJwwZNTKxfuvaX8z-iq0PQKvjlLul-kvJcCAGSCf4Nz4uAQw</recordid><startdate>20150901</startdate><enddate>20150901</enddate><creator>Wang, Xiao Li</creator><creator>Wu, Ga Ridi</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150901</creationdate><title>On n-Widths of a Sobolev Function Class in Orlicz Spaces</title><author>Wang, Xiao Li ; 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| ispartof | Acta mathematica Sinica. English series, 2015-09, Vol.31 (9), p.1475-1486 |
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| 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 |
| title | On n-Widths of a Sobolev Function Class in Orlicz Spaces |
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