| 具有整数伸缩因子的多变量向量值双正交多小波包 |
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| 引用本文： | 朱玉清,卫艳荣,程正兴.具有整数伸缩因子的多变量向量值双正交多小波包[J].郑州大学学报(自然科学版),2012(3):61-65. |
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| 作者姓名： | 朱玉清 卫艳荣 程正兴 |
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| 作者单位： | [1]南阳理工学院数理学院,河南南阳473004 [2]济源职业技术学院基础部,河南济源465650 [3]西安交通大学理学院,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,编号10571113; 陕西省自然科学基金资助项目,编号2009JM1002 |
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| 摘 要： | 研究多变量向量值双正交多小波包的构造与性质.引进了向量值多分辨分析与多变量值双正交多重小波的概念.给出多变量多重向量值双正交小波包的定义及其迭代方法.运用积分变换与有限群理论,讨论了多变量多重向量值双正交小波包的性质,得到了多变量多重向量值双正交小波包的双正交公式,进而给出多变量向量值函数空间L2（Rs,Cn）的一个新的基底.
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| 关 键 词： | 多变量 多重 双正交 向量值多分辨分析 迭代算法 向量值小波包 |
Biorthogonal Vector-valued Multivariable Multiwavelet Packets with an Integer-valued Dilation Factor |
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| ZHU Yu-qing,WEI Yan-rong,CHENG Zheng-xing.Biorthogonal Vector-valued Multivariable Multiwavelet Packets with an Integer-valued Dilation Factor[J].Journal of Zhengzhou University (Natural Science),2012(3):61-65. |
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| Authors: | ZHU Yu-qing WEI Yan-rong CHENG Zheng-xing |
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| Institution: | 1.School of Mathematics and Physics,Nanyang Institute of Technology,Nanyang 473004,China; 2.Department of Fundamentals,Jiyuan Vocational and Technical College,Jiyuan 454650,China; 3.Faculty of Science,Xi＇an Jiaotong University,Xi＇an 710049,China) |
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| Abstract: | The definition of the biorthogonal vector-valued multivariate multiwavelet packets was given and vector-valued multiresolution analysis was introduced.A procedure for construction was presented.The properties for the biorthogonal multiple vector-valued multivariate wavelet packets were investigated by virtue of iterative algorithms and operator theory.Biorthogonality formulas concerning these wavelet packets were formulated.Finally,a new basis of L2（Rs,Cn）was constructed by using the biorthogonal multiple vector-valued multivariate wavelet packets. |
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| Keywords: | multivariable multiple biorthogonal vector-valued multiresolution analysis iterative algorithm vector-valued wavelet packets |
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