Copyright © 2011 Yuan Zhu et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper introduces multiresolution analyses with composite dilations (AB-MRAs) and addresses frame multiresolution analyses with composite dilations in the setting
of reducing subspaces of (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace . For a general expansive matrix, we obtain
the characterizations for a scaling function to generate an AB-RMRA, and the main theorems
generalize the classical results. Finally, some examples are provided to illustrate the general