A-Parseval框架小波的特征刻画

The Characterizations of A-Parseval Frame Wavelet

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.

In this paper, the characterization of Parseval frame wavelets with dilation matrix A （A-PFW）is studied, where A satisfies A^3 = 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 （D-PFW, /9-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.