| The Infinite—dimensional σ—widths of Besov Classes |
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| 引用本文： | 许贵桥,刘永平.The Infinite—dimensional σ—widths of Besov Classes[J].数学进展,2001,30(1):89-90. |
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| 作者姓名： | 许贵桥 刘永平 |
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| 作者单位： | [1]Dept.of [2]Math.,Beijing |
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| 基金项目： | Supported partlyby
Scientific Research Foundation for Returned Overseas Chineses Scholars of the State
Education Ministryof China and partly by Scientific Research Foundation forkey teacher of
the State Education Ministryof China. |
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| 摘 要： | Let (X(Rd),|.|X) be a normed space of real functions on Rd.Let >0 and Pα be the operator in X(Rd) defined by Pα f(x)=χα(x) f(x) (where χα(x) is thecharacteristic function of the cube Idα=［-α,α］d). Let L be asubspace of X(Rd). Set PαL=Pα f:f∈L. Suppose L islocally-finite dimensional, I.e., dim(Pα L,X)<+∞ for every >0.Then the following quantity is said to be the average dimension of L in X(in the sense of LED)(see ［1］).
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| 关 键 词： | 有限维σ－宽 BESOV类 连续线性算子 范数空间 |
The
Infinite-dimensional -widths of Besov Classes |
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| Xu Guiqiao,Liu Yongping.The
Infinite-dimensional -widths of Besov Classes[J].Advances in Mathematics,2001,30(1):89-90. |
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| Authors: | Xu Guiqiao Liu Yongping |
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| Abstract: | |
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