框架和Riesz基的稳定性

On the stabilities of frames and Riesz bases

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L2(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.

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.