Projective multiresolution analyses for dilations in higher dimensions

We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on Rn with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations whose domains are finitely generated projective modules over continuous complex-valued functions on ntori, n ≥ 3. We are able to generalize some of these results to dilation matrices that are conjugates of integral diagonal dilation matrices by elements of SL(n,Z). We follow the method proposed by the author and M. Rieffel, and are able to come up with examples of non-free projective module wavelet frames which can be described via this construction. As an application of our results, in the case n = 3, when the dilation matrix is a constant multiple of the identity, we embed every finitely generated module as an initial module.