中文摘要：

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=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，D相关的Parseval框架小波（D-PFW，D—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（MRAA—PFW）的特征刻画．最后，借助于维数函数，给出了A—PFW是MRAA—PFW的一个充要条件．

英文摘要：

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.