Journal of Operator Theory

Volume 57, Issue 1, Winter 2007 pp. 147-172.

Projective multir esolution analyses for dilations in higher dimensions

Authors: Judith A. Packer
Author institution: Department of Mathematics, CB 395, University of Colorado, Boulder CO, 80309-0395, USA

Summary: We continue the study of projective module wavelet frames corresponding to diago nal dilation matrices on $\mathbb R^n$ with integer entries. We follow the metho d proposed by the author and M. Rieffel, and are able to come up with examples o f non-free projective module wavelet frames which can be described via this cons truction. The construction is generalized to include all integral dilation matri ces that are conjugates of diagonal matrices by elements in $SL(n,\mathbb Z).$ A s 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 projectiv e module of $C(\mathbb T^3)$ as an initial module.

Keywords: Module frames, finitely generated projective modules, dilations, $K$-\break theory, wavelets, $C^*$-algebras, Hilbert $C^*$-module.

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