| N-Widths and Average Widths of Besov Classes in Sobolev Spaces |
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| 作者姓名： | Gui Qiao XU Yong Sheng SUN Yong Ping LIU |
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| 作者单位： | [1]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China [2]School of Mathematical Sciences, Tianjin Normal University, Tianjin 300074, P. R. China |
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| 基金项目： | 1） Supported bY Project （No.10471010） of National Natural Science Foundation of China; 2） Supported by the Development Foundation of Science and Technology of Tianjin Universities （20040405）; 3） Supported by Project ＂Representation Theory and Related Topics＂ of the ＂985 Program＂ of Beijing Normal University; 4） The corresponding author |
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| 摘 要： | In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.
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| 关 键 词： | Besov组 n-宽度 Sobolev空间 平均宽度 |
| 收稿时间： | 2004-07-07 |
| 修稿时间： | 2004-07-072004-11-11 |
N–Widths and Average Widths of Besov Classes in Sobolev Spaces |
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| Gui Qiao XU Yong Sheng SUN Yong Ping LIU.N-Widths and Average Widths of Besov Classes in Sobolev Spaces[J].Acta Mathematica Sinica,2006,22(6):1667-1678. |
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| Authors: | Gui Qiao Xu Yong Sheng Sun Yong Ping Liu |
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| Institution: | (1) School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China;(2) School of Mathematical Sciences, Tianjin Normal University, Tianjin 300074, P. R. China;(3) School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | In this paper, we consider the n–widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov
n–widths, the linear n–widths, the Gel’fand n–widths, in the Sobolev spaces on T
d
, and the infinite–dimensional widths and the average widths in the Sobolev spaces on R
d
are obtained, respectively.
*Supported by Project (No.10471010) of National Natural Science Foundation of China
**Supported by the Development Foundation of Science and Technology of Tianjin Universities (20040405)
***Supported by Project “Representation Theory and Related Topics” of the “985 Program” of Beijing Normal University |
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| Keywords: | Besov class n-width Sobolev space Average width |
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