Property of Nonhomogeneous Dual Wavelet Frames in Reducing Subspaces

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.