约化子空间中非齐次对偶小波标架的一个性质

Property of Nonhomogeneous Dual Wavelet Frames in Reducing Subspaces

为了研究约化子空间中非齐次对偶小波标架的性质,基于约化子空间的任意伸缩和平移不变,运用小波标架的构造方法,证明了不同层次非齐次对偶小波标架之间的等价性,任一非齐次对偶小波标架可以导出一齐次对偶小波标架,而且也获得了非齐次Parseval小波标架类似的性质.

Based on the arbitrary expansion and translation invariance of the reducing subspace and by using the method of construction of wavelet frames, we prove the equivalence among nonhomogeneous dual wavelet frames with arbitrary levels, and the fact that an arbitrary nonhomogeneous dual wavelet frames derives a homogeneous dual wavelet frames. Furthermore, we obtain the similar properties of the nonhomogeneous Parseval wavelet frame.