| 一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波 |
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| 引用本文： | 薛艳梅,毕宁.一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波[J].数学研究及应用,2013,33(2):209-220. |
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| 作者姓名： | 薛艳梅 毕宁 |
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| 作者单位： | 中山大学数学与计算科学学院, 广东 广州 510275;中山大学数学与计算科学学院, 广东 广州 510275; 2. 中山大学广东省计算科学重点实验室, 广东 广州 510275 |
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| 基金项目： | 广东省计算科学重点实验室资助项目. |
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| 摘 要： | 本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.
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| 关 键 词： | 不可分 多变量 正交 紧支撑 稳定性. |
| 收稿时间： | 2011/11/10 0:00:00 |
| 修稿时间： | 2012/2/20 0:00:00 |
A Class of Compactly Supported Nonseparable Orthogonal Wavelets of $L^2(\mathbb{R}^n)$ |
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| Yanmei XUE and Ning BI.A Class of Compactly Supported Nonseparable Orthogonal Wavelets of $L^2(\mathbb{R}^n)$[J].Journal of Mathematical Research with Applications,2013,33(2):209-220. |
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| Authors: | Yanmei XUE and Ning BI |
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| Affiliation: | School of Mathematics and Computational Science, Sun Yat-sen University, Guangdong 510275, P. R. China;School of Mathematics and Computational Science, Sun Yat-sen University, Guangdong 510275, P. R. China; Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangdong 510275, P. R. China |
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| Abstract: | In this paper, we present a concrete method for constructing a class of compactly supported nonseparable orthogonal wavelet bases of $L^{2}(\mathbb{R}^{n}),\ n \geq2$. The orthogonal wavelets are associated with dilation matrix $\alpha I_{n}\ (\alpha\geq2,\ \alpha \in \mathbb{Z})$, where $I_{n}$ is the identity matrix of order $n$. In the end, two examples are given to illustrate how to use our method to construct nonseparable orthogonal wavelet bases. |
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| Keywords: | nonseparable multivariate orthogonal compactly supported stability |
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