| Cgau小波变换像空间中的等距变换与反演公式 |
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| 引用本文： | 李莎莎,邓彩霞,付作娴.Cgau小波变换像空间中的等距变换与反演公式[J].数学年刊A辑(中文版),2011,32(1):121-128. |
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| 作者姓名： | 李莎莎 邓彩霞 付作娴 |
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| 作者单位： | 吉林大学数学研究所;大庆师范学院教学系;哈尔滨理工大学应用数学系; |
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| 基金项目： | 黑龙江省自然科学基金(No.A200902); 黑龙江省博士后基金(No.LBH-Z08102); 哈尔滨理工大学校青年科学基金(No.2009YF034)资助的项目 |
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| 摘 要： | 在以再生核Hilbert空间为连续小波变换像空间的基础上,针对Cgau小波(复数形式的Gauss小波),给出了其小波变换像空间的再生核的具体表达式.当固定尺度因子时,利用再生核空间理论,对Cgau小波变换像空间做了具体描述,分别给出了Cgau小波变换像空间中的等距变换和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.
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| 关 键 词： | 小波变换 再生核 Cgau小波 |
The Isometric Identities and the Inversion Formulas of Image Space of Cgau Wavelet Transform |
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| LI Shash,DENG Caixia and FU Zuoxian.The Isometric Identities and the Inversion Formulas of Image Space of Cgau Wavelet Transform[J].Chinese Annals of Mathematics,2011,32(1):121-128. |
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| Authors: | LI Shash DENG Caixia and FU Zuoxian |
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| Institution: | LI Shasha~1 DENG Caixia~2 FU Zuoxian~2 1 Institute of Mathematics,Jilin University,Changchun 130012,China,Department of Mathematics,Daqing Normal University,Daqing 163712,Heilongjiang,China. 2 Department of Applied Mathematics,Harbin University of Science and Technology,Harbin 150080,China. |
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| Abstract: | The expression of the reproducing kernel function of the image space of the Cgau wavelet transform is shown.When the scale is fixed,a concrete characterization of image space of Cgau wavelet transform is given by the theory of reproducing kernel function.The isometric identities and the inversion formulas are obtained respectively,which provides a theoretical basis to study image space of the general wavelet transform. |
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| Keywords: | Wavelet transform Reproducing kernel Cgau wavelet |
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