二元多重小波紧框架的矩阵频域乘子  

On Matrix Frequency Multipliers Concerning Multiple Tight Bivariate Wavelet Frames

作　　者：宋亮[1] 张桂霞 程正兴[3] 

机构地区：[1]南阳理工学院数理学院,河南南阳473004 [2]三门峡市教师进修学校数学教研室,河南三门峡472000 [3]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2016年第2期270-277,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61403298);河南省自然科学基金(102300410022)

摘　　要：矩阵频域乘子是由本质有界可测函数组成的矩阵,它能将多重小波紧框架映射成多重小波紧框架.引入二元多重小波紧框架的矩阵频域乘子的概念,给出了一个矩阵值函数成为二元多重小波紧框架的矩阵乘子的充要条件,并给出了构造例子.A matrix frequency multiplier is a matrix composed of several essentially bounded measured functions, which can mapp the tight multi-wavelet frames into the tight multi： wavelet frames. The concept for matrix frequency multipliers concerning bivariate tight multi- wavelet frames is introduced in this paper. Based on matrix theory, a sufficient and necessary condition for a matrix-valued function, which becomes matrix frequency multipliers for bi- variate tight multi-wavelet frames is provided. Lots of constructive examples are presented as well.

关 键 词：二元多重小波框架 框架多分辨分析 矩阵傅立叶乘子 框架生成元 矩阵值函数 

分 类 号：O174.2[理学—数学]