| A-Parseval框架小波的特征刻画 |
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| 引用本文： | 黄永东,孙娜.A-Parseval框架小波的特征刻画[J].数学学报,2011(5). |
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| 作者姓名： | 黄永东 孙娜 |
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| 作者单位： | 北方民族大学信息与系统科学研究所; |
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| 基金项目： | 国家自然科学基金资助项目(10961001); 教育部科学技术研究重点项目(209152) |
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| 摘 要： | 研究与伸缩矩阵A相关的Parseval框架小波(A-PFW)的特征刻画,其中伸缩矩阵A满足A~3=2I_3且A的每一列元素之和均为偶数.首先,讨论了与两个特殊伸缩矩阵B,C相关的Parseval框架小波(B-PFW,C-PFW)之间的关系,并得到C-PFW分别与两类特殊伸缩矩阵D,■相关的Parseval框架小波(D-PFW,■-PFW)之间的等价关系.其次,探讨了伪尺度函数和源于多分辨分析的A-PFW(MRA A-PFW)的特征刻画.最后,借助于维数函数,给出了A-PFW是MRA A-PFW的一个充要条件.
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| 关 键 词： | Parseval框架小波 MRA Parseval框架小波 维数函数 |
The Characterizations of A-Parseval Frame Wavelet |
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| Yong Dong HUANG Na SUN Institute of Information , System Science,North University for Nationalities,Yinchuan ,P.R.China.The Characterizations of A-Parseval Frame Wavelet[J].Acta Mathematica Sinica,2011(5). |
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| Authors: | Yong Dong HUANG Na SUN Institute of Information System Science North University for Nationalities Yinchuan PRChina |
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| Institution: | Yong Dong HUANG Na SUN Institute of Information and System Science,North University for Nationalities,Yinchuan 750021,P.R.China |
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| Abstract: | In this paper,the characterization of Parseval frame wavelets with dilation matrix A(A-PFW)is studied,where A satisfies A~3= 2I_3 and the sums of the elements in each column are even number.Firstly,the relation of Parseval frame wavelets with special dilation matrix B(B-PFW) and Parseval frame wavelets with special dilation matrix C(C-PFW) is discussed,and at the same time the equivalence relations of C-PFW) and Parseval frame wavelets with two kinds of special dilation matrices D,■(D-PFW,■-PFW) are gave.Secondly,the characterizations of pseudo-scaling function and MRA Parseval frame wavelets with dilation matrix A(MRA A-PFW) are presented.Finally,by means of dimensional function,a sufficient and necessary condition for an A-PFW to be an MRA A-PFW is obtained. |
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| Keywords: | Parseval frame wavelets MRA Parseval frame wavelets dimensional function |
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