摘要
多分辨分析的概念在小波基构造中起着非常重要的作用,并经历了从经典多分辨分析到多重多分辨分析,再到矩阵值多分辨分析的研究历程.本文基于矩阵值多分辨分析,研究并给出了矩阵值函数空间中尺度空间稠密性的两个充要条件,并在此基础之上得到了稠密性的两个充分条件.
The multiresolution analysis is a very important to construct the wavelet basis. From the classic multiresolution analysis to the multiwavelets multiresolution analysis and the matrix-valued multiresolution analysis, the content of the MRA has been greatly development. In this paper, we discuss the density of the space of matrix-valued scaling function which is based on the space of matrix-valued functions. And finally, we give two necessary and sufficient conditions and two sufficient conditions of the density.
出处
《纯粹数学与应用数学》
CSCD
2012年第2期143-148,共6页
Pure and Applied Mathematics
基金
大学生创新性实验计划(101001027)
关键词
矩阵值多分辨分析
矩阵值函数空间
尺度空间
稠密性
matrix-valued multiresolution analysis, the space of matrix-valued functions, the space of matrix-valued scaling function, density
