Projective multiresolution analyses for dilations in higher dimensions
| dc.creator | Packer, Judith A. | |
| dc.date | 2005-02-25 | |
| dc.date.accessioned | 2026-07-07T05:17:31Z | |
| dc.date.available | 2026-07-07T05:17:31Z | |
| dc.description | We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on $\mathbb R^n$ 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 $n$-tori, $n\geq 3$. We are able to generalize some of these results to dilation matrices that are conjugates of integral diagonal dilation matrices by elements of $SL(n,\mathbb Z).$ 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. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502557 | |
| dc.identifier | http://arxiv.org/abs/math/0502557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74334 | |
| dc.subject | Functional Analysis | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Primary 46L99; Secondary 42C15, 46H25, 19M05 | |
| dc.title | Projective multiresolution analyses for dilations in higher dimensions | |
| dc.type | text |