W~m_2(R~n)中单个函数的平移和伸缩组合的稠密性

蒋传海;陈天平

数学学报 ›› 1999, Vol. 42 ›› Issue (3)

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PDF(436 KB)
数学学报 ›› 1999, Vol. 42 ›› Issue (3) DOI: 10.12386/A1999sxxb0055
论文

W~m_2(R~n)中单个函数的平移和伸缩组合的稠密性

    蒋传海;陈天平
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Denseness of Superposition of One Function with Its Translationand Dilation in Soboley Space W2m(Rn)

    Chuan Hai JIANG(1),Tian Ping C
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摘要

本文讨论单个函数的平移和伸缩的组合在Sobolev空间W2M(Rn)中稠密的问题,得到了稠密的一个充分必要条件,并对于W2m(Rn)中紧集内的函数给出更强的逼近结果。

Abstract

In this paper, we investigate denseness of superposition of one functionwith its translation and dilation in Sobolev space W2m(Rn), and give a necessary andsufficient condition for denseness. Furthermore, we obtain a strong aproximate resultto the functions in any compact set of W2m(Rn).

关键词

Sobofev空间W2M(Rn) / 广义函数 / Fourier变换

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蒋传海;陈天平. W~m_2(R~n)中单个函数的平移和伸缩组合的稠密性. 数学学报, 1999, 42(3) https://doi.org/10.12386/A1999sxxb0055
Chuan Hai JIANG(1),Tian Ping C. Denseness of Superposition of One Function with Its Translationand Dilation in Soboley Space W2m(Rn). Acta Mathematica Sinica, Chinese Series, 1999, 42(3) https://doi.org/10.12386/A1999sxxb0055
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