| WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES |
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| 作者姓名： | 刘永平 许贵桥 |
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| 作者单位： | Department of Mathematics，Beijing Normal University，Department of Mathematics，Beijing Normal University Beijing 100875，China，Beijing 100875，China |
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| 基金项目： | The project is supported partly by the National
Natural Science Foundation of China(10071007)and partly by the Foundation for University Key Teachers by
the Ministry of Education of China and partly by the Scientific Research Foundation for Returned Ov |
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| 摘 要： | This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.
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| 收稿时间： | 11 October 2000 |
WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES |
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| Liu Yongping Xu Guiqiao.WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES[J].Acta Mathematica Scientia,2003,23(2):178-184. |
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| Authors: | Liu Yongping Xu Guiqiao |
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| Institution: | Liu Yongping Xu Guiqiao
Department of Mathematics,Beijing Normal University,Beijing 100875,China |
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| Abstract: | This paper concerns the problem of the Kolmogorov n-width, the linear n-width, the Gel'fand n-width and the Bernstein n-width of Sobolev classes of the periodicmultivariate functions in the space Lp(Td) and the average Bernstein σ-width, averageKolmogorov σ-widths, the average linear σ-widths of Sobolev classes of the multivariatequantities. |
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| Keywords: | Multivariate function Sobolev class width average width |
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