| 高维小波框架包子空间对空间L2(Rn)的分解 |
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| 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. |
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| 作者姓名： | 盖晓华 郭学军 冯金顺 陈清江 程正兴 |
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| 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 |
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| 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) |
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| 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。
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| 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 |
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| 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. |
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| Authors: | GAI Xiao-hua GUO Xue-jun FENG Jin-shun CHEN Qing-jiang CHENG Zheng-xing |
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| Institution: | 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, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China;4. School of Mathematics and Statistics, Xian Jiaotong University, Xian 710049, Shaanxi, China |
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| 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. |
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| Keywords: | wavelet frames framelet packets expansion principle mask functions generators |
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