LI Wan-she, GUO Xiao-xuan
(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
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 L2(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
