矩阵伸缩的高维向量值小波包

Multivariate Vector-valued Wavelet Packets Associated with the Dilation Matrix

中文关键词:  伸缩矩阵  向量值多分辨分析  向量值尺度函数  向量值小波包  加细方程.

英文关键词:dilation matrix  vector-valued multiresolution analysis  vector-valued scaling functions  vector-valued wavelet packets  refinement equation

中文摘要:

      本文给出了对应于任意整数矩阵伸缩的高维向量值正交小波包的定义及其构造方法.并讨论了这种向量值正交小波包的性质,得到向量值函数空间$L^2({\bf R}^s,{\bf C}^r)$的新的正交小波基.

英文摘要:

      In this paper,\,we introduce the notion of orthogonal vector-valued wavelet packets in higher dimensions associated with a given integer-valued dilation matrix. A procedure for constructing the orthogonal multivariate vector-valued wavelet packets is presented. The properties of the multivariate vector-valued wavelet packets have been discussed. Moreover, several new orthogonal bases of $L^2({\bf R}^s,{\bf C}^r)$ are constructed by using the orthogonal vector-valued wavelet packets.