A Hilbert C*-module for Gabor systems
| dc.creator | Coco, Michael | |
| dc.creator | Lammers, M. C. | |
| dc.date | 2001-02-20 | |
| dc.date.accessioned | 2026-07-07T04:40:17Z | |
| dc.date.available | 2026-07-07T04:40:17Z | |
| dc.description | We construct Hilbert $C^*$-modules useful for studying Gabor systems and show that they are Banach algebras under pointwise multiplication. For rational $ab<1$ we prove that the set of functions $g \in L^2(R)$ so that $(g,a,b)$ is a Bessel system is an ideal for the Hilbert $C^*$-module given this pointwise algebraic structure. This allows us to give a multiplicative perturbation theorem for frames. Finally we show that a system $(g,a,b)$ yields a frame for $L^2(R)$ iff it is a modular frame for the given Hilbert $C^*$-module. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0102165 | |
| dc.identifier | http://arxiv.org/abs/math/0102165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60979 | |
| dc.subject | Functional Analysis | |
| dc.title | A Hilbert C*-module for Gabor systems | |
| dc.type | text |