JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (8): 34-42.doi: 10.6040/j.issn.1671-9352.0.2018.058

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Decomposition for L2(Rn)by subspaces composed of high-dimensional tight framelet packets

GAI Xiao-hua1, GUO Xue-jun2*, FENG Jin-shun2, CHEN Qing-jiang3, CHENG Zheng-xing4   

  1. 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
  • Received:2018-01-31 Online:2018-08-20 Published:2018-07-11

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.

Key words: wavelet frames, framelet packets, expansion principle, mask functions, generators

CLC Number: 

  • O174.2
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