| 多小波子空间上的单小波表示 |
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| 引用本文： | 崔丽鸿,程正兴.多小波子空间上的单小波表示[J].数学学报,2003,46(4):691-696. |
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| 作者姓名： | 崔丽鸿 程正兴 |
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| 作者单位： | 西安交通大学理学院西安710049 |
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| 摘 要： | 本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.
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| 关 键 词： | 单小波 2重多小波 Riesz基 Shannon型采样定理 插值 |
| 文章编号： | 0583-1431(2003)04-0691-06 |
| 修稿时间： | 2002年1月23日 |
Representation for Multiwavelets Subspaces by the Uni-Wavelet |
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| Li Hong GUI Zheng Xing CHENG.Representation for Multiwavelets Subspaces by the Uni-Wavelet[J].Acta Mathematica Sinica,2003,46(4):691-696. |
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| Authors: | Li Hong GUI Zheng Xing CHENG |
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| Institution: | Li Hong GUI Zheng Xing CHENG (School of Sciences, Xz'an Jiaotong University, Xi'an 710049, P. R. China) |
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| Abstract: | Under weak hypotheses, we establish the relation between multiwavelets subspaces with multiplicity 2 and uni-wavelet subspaces, i.e., the uni-wavelet is constructed by multiwavelets with multiplicity 2. On the one hand, the subspace generated by translates and dilations of the uni-wavelet is the same as the subspace generated by multiwavelets with multiplicity 2; on the other hand, the uni-wavelet also possesses the interpolatory property. Based on uni-wavelet generated by our method, the Shan-non'type sampling theorem on the multiwavelets subspace is presented. |
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| Keywords: | Uni-wavelet Multiwavelet with multiplicity 2 Riesz basis Shannon's type sampling theorem Interpolatory |
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