Minimum-energy multi-wavelets tight frames associated with two scaling functions

At present, there is little research on multi-wavelets tight frames. We study minimum-energy multi-wavelets tight frames which correspond to two scaling functions with compact supports, and give a existence criterion for minimum-energy multi-wavelets tight frames, if the scaling functions of the minimum-energy multi-wavelets tight frames changed by an orthogonal matrix, the new scaling functions also can generate a minimum-energy multi-wavelets tight frames.