Abstract:

 The theory of frames is very important for wavelet　analysis. For φ∈L²(R) and a>1, b>0, I.Daubechies gave a sufficient condition ensuring{a^j/2}φ(a^j 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　φ, {a^j} and {k} have some perturbation simultaneously.In particular, we study the effect of the perturbation to {a^j}.

Key words: Ｆｒａｍｅｓ, Ｗａｖｅｌｅｔｓ, Ｋａｄｅｃ＇ｓ１／４－ｔｈｅｏｒｅｍ．