A characterizition of MRA super-wavelets

The MRA super-wavelet theory was investigated in the direct sum Hilbert space L²(R)^(m)=Sigma_j=1 ^moplusL²(R). It is shown that a super-wavelet arises from our MRA construction if and only if the dimension of each particular linear space is either zero or one. In particular, when E_i is a bounded normalized tight frame wavelet set, it is shown that a super-wavelet arise from our MRA construction if and only if E_i ^s =cup_kges12^-k E_i is 2pi - translation congruent to a subset of [-pi, pi]. In addition, an example is given.