Projective multiresolution analyses for $L^2(R^2)$
| dc.creator | Packer, Judith A. | |
| dc.creator | Rieffel, Marc A. | |
| dc.date | 2003-08-14 | |
| dc.date | 2004-03-09 | |
| dc.date.accessioned | 2026-07-07T05:00:23Z | |
| dc.date.available | 2026-07-07T05:00:23Z | |
| dc.description | We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra $C(\btn)$ of continuous complex-valued functions on an $n$-torus. The case of ordinary multi-wavelets is that in which the projective module is actually free. We discuss the properties of projective multiresolution analyses, including the frames which they provide for $L^2(\brn)$. Then we show how to construct examples for the case of any diagonal $2 \times 2$ dilation matrix with integer entries, with initial module specified to be any fixed finitely generated projective $C(\mathbb T^2)$-module. We compute the isomorphism classes of the corresponding wavelet modules. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308132 | |
| dc.identifier | http://arxiv.org/abs/math/0308132 | |
| dc.identifier | J. Fourier Anal. Appl. 10 (2004), no. 5, 439--464. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68311 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L99; 42C15;46H25;47A05 | |
| dc.title | Projective multiresolution analyses for $L^2(R^2)$ | |
| dc.type | text |