一类多重小波紧框架的特征刻画  

Characterizations of a class of multi-wavelet tight framelets

作　　者：吴宏锷[1] 梁瑛[1] 程正兴[2] 

机构地区：[1]南阳理工学院数理学院,河南南阳473004 [2]西安交通大学理学院,陕西西安710049

出　　处：《兰州理工大学学报》2014年第4期145-149,共5页Journal of Lanzhou University of Technology

基　　金：河南省自然科学基金(102300410022)

摘　　要：刻画多重小波紧框架的特征.引入对应于多重加细函数的多重小波框架的概念.给出多重小波紧框架存在的充要条件.通过对加细函数向量作傅里叶变换得到矩阵符号,运用矩阵理论,给出生成多重小波紧框架的加细函数向量所满足的条件.对原加细函数向量和多重小波紧框架做正交变换,得到新的加细函数向量和与之对应的多重小波紧框架生成元.The multi-wavelet tight framelets are characterized. The concept of a multi-wavelet tight fra- reelers associated with a refinable function is introduced. The sufficient and necessary condition for existence of multi-wavelet tight framelets is given. The matrix symbols are obtained by using Fourier transform from a refinable function vector. The conditions satisfied by the refinable function vector of multiwavelet tight framelets are given with the help of matrix theory. A new refinable function vector and its corresponding generation element of multi-wavelet tight framelets are obtained by means of orthogonal transform from the original refinable function vector into multi-wavelet tight framelets.

关 键 词：小波紧框架 框架生成元 正交变换 框架多分辨分析 

分 类 号：O174.2[理学—数学]