高维小波框架包子空间对空间L^2(R^n)的分解  

Decomposition for L^2( R^n) by subspaces composed of high-dimensional tight framelet packets

作　　者：盖晓华[1] 郭学军 冯金顺 陈清江[3] 程正兴[4] GAI Xiao-hua;GUO Xue-jun;FENG Jin-shun;CHEN Qing-jiang;CHENG Zheng-xingg(School of Electronic and Electrical Engineering,Nanyang Institute of Technology,Nanyang 473004,Henan,China;School of Mathematics and Statistics,Nanyang Institute of Technology,Nanyang 473004,Henan,China;School of Science,Xi＇an University of Architecture and Technology,Xi＇an 710055,Shaanxi,China;School of Mathematics and Statistics,Xi＇an Jiaotong University,Xi＇an 710049,Shaanxi,China)

机构地区：[1]南阳理工学院电子与电气工程学院,河南南阳473004 [2]南阳理工学院数学与统计学院,河南南阳473004 [3]西安建筑科技大学理学院,陕西西安710055 [4]西安交通大学数学与统计学院,陕西西安710049

出　　处：《山东大学学报（理学版）》2018年第8期34-42,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61504072);河南省自然科学基金资助项目(102300410022)

摘　　要：研究小波框架包子空间对空间L^2(R^n)的分解。运用时频分析方法与逼近论思想,刻画了数量矩阵伸缩的高维小波框架包的特征,构造了若干高维小波框架包子空间,进而,由小波框架包子空间得到了L^2(R^n)的直交分解式。给出高维小波框架包函数的频域表达式,类似于正交基,提出高维紧小波框架包构成空间L^2(R^n)的巴塞尔框架的充分条件,扩展了小波框架应用范围。The decomposition for space L2（ Rn） by subspaces composed of framelet packets are investigated. The characteristics of the high-dimensional wavelet frame packets with a quantity dilation matrix are described by using time-frequency analysis method and functional analysis method. The subspaces from the high-dimensional framelet packets are constructed. Moreover the direct decomposition for space L2（ Rn） is obtained from these subspaces composed of framelet packets. The frequency-field formulas for the high-dimensional framelet packets are presented. A sufficient condition is suggested that a Parseval frame constituted from the high-dimensional tight framelet packets of space L2（ Rn）. These enrich the wavelet frame theory,so that they can be applied to a wider range.

关 键 词：小波框架 小波框架包 面具函数 扩张原理 生成元 

分 类 号：O174.2[理学—数学]