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高维小波框架包子空间对空间L2(Rn)的分解
引用本文:盖晓华,郭学军,冯金顺,陈清江,程正兴. 高维小波框架包子空间对空间L2(Rn)的分解[J]. 山东大学学报(理学版), 2018, 53(8): 34-42. DOI: 10.6040/j.issn.1671-9352.0.2018.058
作者姓名:盖晓华  郭学军  冯金顺  陈清江  程正兴
作者单位: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
基金项目: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L2(Rn)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L2(Rn)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L2(Rn)的巴塞尔框架的充分条件,扩展了小波框架应用范围。

关 键 词:面具函数  扩张原理  生成元  小波框架  小波框架包  
收稿时间:2018-01-31

Decomposition for L2(Rn)by subspaces composed of high-dimensional tight framelet packets
GAI Xiao-hua,GUO Xue-jun,FENG Jin-shun,CHEN Qing-jiang,CHENG Zheng-xing. Decomposition for L2(Rn)by subspaces composed of high-dimensional tight framelet packets[J]. Journal of Shandong University, 2018, 53(8): 34-42. DOI: 10.6040/j.issn.1671-9352.0.2018.058
Authors:GAI Xiao-hua  GUO Xue-jun  FENG Jin-shun  CHEN Qing-jiang  CHENG Zheng-xing
Affiliation:1. School of Electronic and Electrical Engineering, Nanyang Institute of Technology, Nanyang 473004, Henan, China; 2. School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan, China;3. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China;4. School of Mathematics and Statistics, Xian Jiaotong University, Xian 710049, Shaanxi, China
Abstract: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.
Keywords:wavelet frames  framelet packets  expansion principle  mask functions  generators  
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