Frame Wavelets with Compact Supports for L^2(R^n) |
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作者姓名: | De Yun YANG King Wei ZHOU Zhu Zhi YUAN |
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作者单位: | [1]Department of Information, Taishan University, Taian 271000, P. R. China [2]Department of Automation, Nankai University, Tianjin 300071, P. R. China [3]Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China |
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基金项目: | Supported by National Natural Science Foundation of China (Grants Nos. 60572113, 60472042) and China Postdoctoral Science Foundation (Grant No. 2004036368),Acknowledgments The authors would like to thank the referees for their useful suggestions and comments. |
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摘 要: | The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.
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关 键 词: | 傅里叶变换 小波分析 扩展矩阵 标架 紧支柱 |
修稿时间: | 2005-08-182006-03-30 |
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