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框架和Riesz基的稳定性
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(自然科学版), 2006, 34(4): 7-12
作者姓名:李万社  郭晓旋
作者单位:陕西师范大学数学与信息科学学院,陕西西安710062
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.

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
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
Authors:LI Wan-she  GUO Xiao-xuan
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.
Keywords:stability   frame   Riesz basis   wavelet frame   wavelet Riesz basis
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