On the stability of multi-wavelet frames

Frame plays an important role in the theory of wavelet analysis. Frame theory and stability of frames are important topics of wavelet analysis. Recently, people pay more attention to multi-wavelet frames. Among literatures, Chui[2], for instance, give a complete characterization of multi-wavelet frames for arbitrary dilation factor a > 1. There, however, is relatively less results on the stability of multi-wavelet frames. This paper devotes to the study of stability of multi-wavelet frames based on functional analysis methods. The following meaningful results are obtained: firstly, multi-wavelet frames are stable by some kinds of linear operators action; Secondly, multi-wavelet frames are stable over some kinds of perturbations conditions on psi.