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小波标架的稳定性
On the Stability of Wavelet Frames
【摘要】 在小波分析理论中,标架起着十分重要的作用.对(∈L2(R)和a>1.b>0,I.Daubechies给出了{aj/2((ajx—kb):j,k ∈Z}构成L2(R)的标架的充分条件.近年来,人们对小波标架的稳定性进行了大量研究.首先把Kadec定理推广到高维情形,然后研究当(,{aj},{k}同时变化时标架的稳定性.特别地,我们给出{aj}扰动时标架的稳定性.
【Abstract】 The theory of frames is very important for wavelet analysis. For ( ∈ L2(R) and a > 1, b > 0, I. Daubechies gave a sufficient condition ensuring {aj/2 ((aj x - kb): j, k ∈ Z } to be a frame for L2(R). Recently, much effort has spent on the study of the stability of wavelet frames. In this paper, after obtaining a multivariate version of Kadec’s 1/4- theorem, we study the stability of wavelet frames when (, {aj} and {k} have some perturbation simultaneously. In particular, we study the effect of the perturbation to {aj}.
【基金】 国家自然科学基金!16971047
- 【文献出处】 数学物理学报 ,ACTA MATHEMATIEA SCIENTIA , 编辑部邮箱 ,1999年02期
- 【分类号】O174
- 【被引频次】17
- 【下载频次】146