| SPECTRAL APPROXIMATION ORDERS OF MULTIDIMENSIONAL NONSTATIONARY BIORTHOGONAL SEMI-MULTIRESOLUTION ANALYSIS IN SOBOLEV SPACE |
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| 作者姓名： | Wen-sheng Chen Chen Xu Wei Lin |
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| 作者单位： | [1]Department of Mathematics, Shenzhen University, Shenzhen 518060, China [2]Key Laboratory of Mathematics Mechanization, CAS, Beijing 100080, China [3]Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China |
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| 基金项目： | This work is partially supported by the National Grand Fundamental Research 973 Program of China under Grant No.G2000078403. |
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| 摘 要： | Subdivision algorithm （Stationary or Non-stationary） is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory. In multidimensional non-stationary situation, its limit functions are both compactly supported and infinitely differentiable. Also, these limit functions can serve as the scaling functions to generate the multidimensional non-stationary orthogonal or biorthogonal semi-multiresolution analysis （Semi-MRAs）. The spectral approximation property of multidimensional non-stationary biorthogonal Semi-MRAs is considered in this paper. Based on nonstationary subdivision scheme and its limit scaling functions, it is shown that the multidimensional nonstationary biorthogonal Semi-MRAs have spectral approximation order r in Sobolev space H^s（R^d）, for all r ≥ s ≥ 0.
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| 关 键 词： | 不稳定细分算法 双正交 谱逼近 Sobolev空间 |
| 收稿时间： | 2005-02-22 |
| 修稿时间： | 2005-02-222005-04-04 |
SPECTRAL APPROXIMATION ORDERS OF MULTIDIMENSIONAL NONSTATIONARY BIORTHOGONAL SEMI-MULTIRESOLUTION ANALYSIS IN SOBOLEV SPACE |
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| Wen-sheng Chen Chen Xu Wei Lin.SPECTRAL APPROXIMATION ORDERS OF MULTIDIMENSIONAL NONSTATIONARY BIORTHOGONAL SEMI-MULTIRESOLUTION ANALYSIS IN SOBOLEV SPACE[J].Journal of Computational Mathematics,2006,24(1):81-90. |
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| Authors: | Wen-sheng;Chen;Chen;Xu;Wei;Lin |
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| Abstract: | Subdivision algorithm(Stationary or Non-stationary)is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory.In multidi- mensional non-stationary situation,its limit functions are both compactly supported and infinitely differentiable.Also,these limit functions can serve as the scaling functions to gen- erate the multidimensional non-stationary orthogonal or biorthogonal semi-multiresolution analysis(Semi-MRAs).The spectral approximation property of multidimensional non- stationary biorthogonal Semi-MRAs is considered in this paper.Based on nonstationary subdivision scheme and its hmit scaling functions,it is shown that the multidimensional nonstationary biorthogonal Semi-MRAs have spectral approximation order r in Sobolev space H~s(R~d),for all r(?)s(?)0. |
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| Keywords: | Nonstationary subdivision algorithm Biorthogonal Semi-MRAs Wavelets Spectral approximation Sobolev space |
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