不规则多小波框架的稳定性

Stability of Irregular Multi-Wavelet Frames

对{ψl:1≤l≤r}施加一定的条件,当伸缩因子{al,j:1≤l≤r,j∈Z}和平移因子{bl,j,k:1≤l≤r,j,k∈Z}扰动时,小波系统{al1,/j2ψl(al,j(.-bl,j,k)):1≤l≤r,j,k∈Z}仍构成L2(R)的框架.

Under certain assumptions an irregular wavelet frame {al1,/j2ψl（al,j（.-bl,j,k））：1≤l≤r,j,k∈Z} in L2 （R） remains a frame when the dilation sequences {al,j：1≤l≤r,j∈Z} and the translation parameters {bl,j,k：1≤l≤r,j,k∈Z} are perturbed.