A-Parseval框架小波的特征刻画

黄永东, 孙娜

数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 767-790.

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数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 767-790. DOI: 10.12386/A2011sxxb0080
论文

A-Parseval框架小波的特征刻画

    黄永东, 孙娜
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The Characterizations of A-Parseval Frame Wavelet

    Yong Dong HUANG, Na SUN
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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A3=2I3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.  

Abstract

In this paper, the characterization of Parseval frame wavelets with dilation matrix A (A-PFW)is studied, where A satisfies A3 = 2I3 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.  

关键词

Parseval框架小波 / MRA Parseval框架小波 / 维数函数

Key words

Parseval frame wavelets / MRA Parseval frame wavelets / dimensional function

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黄永东, 孙娜. A-Parseval框架小波的特征刻画. 数学学报, 2011, 54(5): 767-790 https://doi.org/10.12386/A2011sxxb0080
Yong Dong HUANG, Na SUN. The Characterizations of A-Parseval Frame Wavelet. Acta Mathematica Sinica, Chinese Series, 2011, 54(5): 767-790 https://doi.org/10.12386/A2011sxxb0080

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基金

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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