矩阵值函数空间中尺度空间的稠密性  

The density of the space of matrix-valued scaling function

作　　者：崔丽鸿[1] 陈晓东[1] 杜俊峰[1] 王隆玉[1] 郭兴宝[1] 崔月娥[1] 

机构地区：[1]北京化工大学理学院数学系,北京100029

出　　处：《纯粹数学与应用数学》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)

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.

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 

分 类 号：O174.2[理学—数学]