A study on minimum-energy vector-valued wavelet tight frames

In this paper, minimum-energy vector-valued wavelet tight frames are introduced. As we know, there are some researches on wavelet frames and multi-wavelets tight frames, however, research on vector-valued wavelet tight frames is very little. With the definition of vector-valued multiresolution analysis [9] and wavelet frame, the study on minimum-energy vector-valued wavelet tight frames which correspond to vector-valued scaling functions with compact supports can be given out. We focus on finding a sufficient condition of the existence of minimum-energy vector-valued wavelet tight frames. In particular, a property of the minimum-energy vector-valued wavelet tight frames will be investigated by multiplied on the left side of the vector-valued scaling functions.