| The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness |
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| 作者姓名： | Yong-ping Liu Gui-qiao Xu |
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| 作者单位： | Yong-ping Liu，Gui-qiao XuDepartment of Mathematics，Beijing Normal University，Beijing 100875，China Department of Mathematics，Tianjin Normal Univesity，Tianjin 300074. China |
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| 基金项目： | the National Natural Science Foundation of China (No.10071007)，partly by Scientific Research Foundation for Returned Overseas Chineses Scholars of the State Education Ministry of China，partly by Scientific Research Foundation for Key Teachers of th |
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| 摘 要： | The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.
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The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness |
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| Yong-ping Liu,Gui-qiao Xu.The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness[J].Acta Mathematicae Applicatae Sinica,2002,18(4):663-674. |
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| Authors: | Yong-ping Liu Gui-qiao Xu |
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| Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, China (E-mail: ypliu@bnu.edu.cn), CN;(2) Department of Mathematics, Tianjin Normal Univesity, Tianjin 300074, China, CN |
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| Abstract: | Abstract
The classes of the multivariate functions with bounded moduli on R
d
and T
d
are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.
* Partly supported by the National Natural Science Foundation of China (No. 10071007) and partly by Scientific Research Foundation
for Returned Overseas Chineses Scholars of the State Education Ministry of China, and partly by Scientific Research Foundation
for Key Teachers of the State Education Ministry of China. |
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| Keywords: | Multivariate function classes average width non-linear width |
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