摘要
研究L2(Rd)中A伸缩的Parseval框架小波的性质,这里的A指的是行列式值取自然数的任意d×d阶扩展矩阵.首先,给出框架小波为半正交时的充要条件,然后证明Parseval框架小波为半正交的充要条件,得到所有基于广义多分辨分析(GMRA)的Parseval框架小波等价于闭子空间W0的Parseval框架为{TkΨ:k∈Zd}的条件.
This paper studies Parseval frame wavelets（PFWs） in L^2 （R^d） with A dilations, where A is an arbitrary expanding d × d matrix, such that det A = c, c ∈ N. Firstly, we prove that a necessary and sufficient condition for the frame wavelet is a semi-orthogonal frame wavelet, and that a necessary and sufficient condition for the Parseval frame wavelet is a semi-orthogonal Parseval frame wavelet. It is observed that all PFWs associated with generalized multiresolution analysis （GMRA） are equivalent to a closed subspace W0 for which （TkΨ：k ∈ Z^d} is a Parseval frame.
出处
《河南大学学报（自然科学版）》
CAS
北大核心
2009年第5期441-445,共5页
Journal of Henan University:Natural Science
