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The Spectrum Sequences of Periodic Frame Multiresolution Analysis 认领 引用
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作者 Yun Zhang LI Qiao Fang LIAN 《Acta Mathematica Sinica,English Series》 SCIE 2009年第3期403-418,共16页
The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. Th... The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory. 展开更多
关键词 PFMRA periodic wavelet frame scaling function sequence spectrum spectrum sequence
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Characterization of Periodic Multiresolution Analysis and an Application 认领 引用
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作者 Li Dengfeng Peng Silong, Institute of Mathematics, Academia Sinica, Beijing 100080, China 《Acta Mathematica Sinica,English Series》 SCIE 1998年第4期547-554,共8页
In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from... In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end. 展开更多
关键词 Wavelet Periodic multiresolution analysis Scaling function sequence
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