| 框架和Riesz基的稳定性 |
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| 引用本文： | 李万社,郭晓旋.框架和Riesz基的稳定性[J].陕西师范大学学报,2006,34(4):7-12. |
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| 作者姓名： | 李万社 郭晓旋 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062 |
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| 摘 要： | 从两方面讨论了Hilbert空间中框架和Riesz基的稳定性：在满足一定条件Bessel序列的扰动下，框架和Riesz基在Hilbert空间中的稳定性；把框架和Riesz基与小波结合起来，在母小波、采样序列的扰动下，小波框架和小波Riesz基在L^2（R）空间中的稳定性．对有关文献的相关结论进行了推广，目的在于可以根据框架的稳定性，设计或者选择一个更优的框架来精确地逼近信号．
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| 关 键 词： | 稳定性 框架 Riesz基 小波框架 小波Riesz基 |
| 文章编号： | 1672-4291（2006）04-0007-06 |
| 收稿时间： | 2006-03-20 |
| 修稿时间： | 2006-03-20 |
On the stabilities of frames and Riesz bases |
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| LI Wan-she,GUO Xiao-xuan.On the stabilities of frames and Riesz bases[J].Journal of Shaanxi Normal University: Nat Sci Ed,2006,34(4):7-12. |
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| Authors: | LI Wan-she GUO Xiao-xuan |
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| Abstract: | The stabilities of frames and Riesz bases are discussed in two aspects.First,the stabilities of frames and Riesz bases perturbated by a Bessel sequence with some conditions in Hilbert space are considered.Secondly,the stabilities of wavelet frames and Riesz bases perturbated by a mother wavelet and a sampling sequence in L~2(R) are discussed,respectively.Our results generalize some related theorems in order to design or choose a more superior frame and achieve more precise approximation to a signal according to the stability of a frame. |
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| Keywords: | stability frame Riesz basis wavelet frame wavelet Riesz basis |
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