A Decomposition Theorem for frames and the Feichtinger Conjecture
| dc.creator | Casazza, Peter G. | |
| dc.creator | Kutyniok, Gitta | |
| dc.creator | Speegle, Darrin | |
| dc.creator | Tremain, Janet C. | |
| dc.date | 2007-02-08 | |
| dc.date.accessioned | 2026-07-07T07:45:36Z | |
| dc.date.available | 2026-07-07T07:45:36Z | |
| dc.description | In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is $ω$-independent for $\ell_2$-sequences. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702216 | |
| dc.identifier | http://arxiv.org/abs/math/0702216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123581 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46C05; 42C15; 46L05 | |
| dc.title | A Decomposition Theorem for frames and the Feichtinger Conjecture | |
| dc.type | text |