Frames and Oversampling Formulas for Band Limited Functions
| dc.creator | Del Prete, Vincenza | |
| dc.date | 2008-08-10 | |
| dc.date | 2008-12-21 | |
| dc.date.accessioned | 2026-07-07T12:20:39Z | |
| dc.date.available | 2026-07-07T12:20:39Z | |
| dc.description | In this article we obtain families of frames for the space B_ωof functions with band in [-ω,ω] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant, due to Bownik, of their characterization of families of functions whose shifts form frames or Riesz bases. We give necessary and sufficient conditions for the translates of a finite number of functions (generators) to be a frame or a Riesz basis for B_ω. We also give explicit formulas for the dual generators and we apply them to Hilbert transform sampling and derivative sampling. Finally, we provide numerical experiments which support the theory. | |
| dc.description | 28 pages, 9 figures; corrected typos | |
| dc.identifier | https://arxiv.org/abs/0808.1412 | |
| dc.identifier | http://arxiv.org/abs/0808.1412 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213126 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42C15; 46E20; 46E22 | |
| dc.title | Frames and Oversampling Formulas for Band Limited Functions | |
| dc.type | text |