| 离散空间■~2(Z)中正交小波系的完备性 |
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| 引用本文： | 蒋英春,刘有明.离散空间■~2(Z)中正交小波系的完备性[J].数学学报,2006(5). |
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| 作者姓名： | 蒋英春 刘有明 |
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| 作者单位： | 北京工业大学应用数学系，北京工业大学应用数学系 北京 100022，北京 100022 |
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| 基金项目： | 北京市教委基金资助项目(KM200410005013) |
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| 摘 要： | 本文研究2(Z)中正交小波系的完备性,其主要目的是寻找一些容易验证的充分条件．为此,我们首先改进了Frazier的定理,给出小波系完备的一个刻画,然后在此基础上得到三个容易验证的充分条件．
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| 关 键 词： | 小波系 完备性 离散傅立叶变换 |
The Completeness of Orthogonal Wavelet Systems in (?)~2(Z) |
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| Ying Chun JIANG You Ming LIU.The Completeness of Orthogonal Wavelet Systems in (?)~2(Z)[J].Acta Mathematica Sinica,2006(5). |
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| Authors: | Ying Chun JIANG You Ming LIU |
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| Institution: | Ying Chun JIANG You Ming LIU Department of Applied Mathematics,Beijing University of Technology,Beijing 100022,P. R. China |
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| Abstract: | This paper studies the completeness of orthogonal wavelet systems in (?)2(Z), the main purpose is to find some easily checked sufficient conditions. To do that, the construction for p stage wavelet bases is firstly revisited; then a characterization for a wavelet system to be complete is shown, which improves Frazier's theorem, three sufficient conditions are finally received from that characterization. |
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| Keywords: | wavelet systems completeness discrete Fourier transform |
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