| Adaptive widths of the approximation functional on the Sobolev space W r 2 with Gaussian measure |
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| 作者姓名： | FANG Gensun YE Peixin |
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| 作者单位： | Department of Mathematics, Beijing Normal University, Beijing 100875, China,Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (Grant No. 10071006) and Research Fund for the Doctoral Program Higher Education. We would like to thank the referees for their extensive comments and excellent suggestions. |
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| 摘 要： | The tight orders for the Kolmogorov and adaptive (n,ε,δ)-widths of the Sobolev spaces W?r?2 equipped with a Gaussian measure in the L1-norm and L∞-norm are determined by the method of discretization, which is based on reducing the calculation of the (n,ε,δ)-widths of the Sobolev space to the calculation of (n,ε,δ)-widths of finite-dimensional set equipped with the Gaussian measure.
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| 关 键 词： | Kolmogorov (n ε δ)-widths non-adaptive and adaptive Gaussian measure |
Adaptive widths of the approximation functional on the Sobolev space W r 2 with Gaussian measure |
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| FANG Gensun,YE Peixin.Adaptive widths of the approximation functional on the Sobolev space W r 2 with Gaussian measure[J].Progress in Natural Science,2002,12(7):506-511. |
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| Authors: | Fang Gensun YE Peixin |
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| Institution: | Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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| Abstract: | The tight orders for the Kolmogorov and adaptive (n,ε,δ)-widths of the Sobolev spaces Wr2 equipped with a Gaussian measure in the L1-norm and L∞-norm are determined by the method of discretization, which is based on reducing the calculation of the (n,ε,δ)-widths of the Sobolev space to the calculation of (n,ε,δ)-widths of finite-dimensional set equipped with the Gaussian measure. |
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| Keywords: | Kolmogorov (n non-adaptive and adaptive Gaussian measure |
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