| L^2（R^2，H；dx）上以实值内积定义的连续小波变换 |
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| 引用本文： | 李亚峰. L^2（R^2，H；dx）上以实值内积定义的连续小波变换[J]. 宝鸡文理学院学报(自然科学版), 2008, 28(4): 274-276 |
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| 作者姓名： | 李亚峰 |
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| 作者单位： | 宝鸡文理学院,计算机科学系,陕西,宝鸡,721007 |
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| 基金项目： | 宝鸡文理学院科研项目 |
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| 摘 要： | 目的建立平方可积的四元数函数空间L^2（R^2，H；dx）上的连续小波变换的Parseval等式及反方程。方法定义四元数集合的实值内积，将空间L^2（R^2，H；dx）分解成为不可约不变子空间的直和，给出容许条件的特征。结果建立了四元数值函数空间小波变换的Parseval等式。结论在弱的意义下给出了小波变换的反方程。
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| 关 键 词： | 四元数 连续小波变换 容许条件 反方程 |
Continuous wavelet transform on the space L~2(R~2,H;dx) by defining real valued inner product |
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| LI Ya-feng. Continuous wavelet transform on the space L~2(R~2,H;dx) by defining real valued inner product[J]. Journal of Baoji College of Arts and Science(Natural Science Edition), 2008, 28(4): 274-276 |
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| Authors: | LI Ya-feng |
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| Affiliation: | Department of Computer Science;Baoji University of Arts and Sciences;Baoji 721007;Shaanxi;China |
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| Abstract: | Aim To establish the Parseval's formula and reconstruction formula for the continuous wavelet transform on the space L2(R2,H;dx).Methods By using real valued inner product on H,L 2(R2,H;dx) was decomposed into the direct sum of the irreducible invariant subspaces and the characterization of the admissibility condition was given.Results This paper establish the Parseval's formula for the continuous wavelet transform on L2(R2,H;dx).Conclusion The inverse wavelet transform in the weak sense was get. |
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| Keywords: | quaternion continuous wavelet transform admissibility condition inverse formula |
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