Gabor fields and wavelet sets for the Heisenberg group
| dc.creator | Currey, Bradley | |
| dc.creator | Mayeli, Azita | |
| dc.date | 2009-03-28 | |
| dc.date | 2009-05-19 | |
| dc.date.accessioned | 2026-07-07T13:15:49Z | |
| dc.date.available | 2026-07-07T13:15:49Z | |
| dc.description | We study singly-generated wavelet systems on $\Bbb R^2$ that are naturally associated with rank-one wavelet systems on the Heisenberg group $N$. We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset $I$ of the dual of $N$, we give an explicit construction for Parseval frame wavelets that are associated with $I$. We say that $g\in L^2(I\times \Bbb R)$ is Gabor field over $I$ if, for a.e. $λ\in I$, $|λ|^{1/2} g(λ,\cdot)$ is the Gabor generator of a Parseval frame for $L^2(\Bbb R)$, and that $I$ is a Heisenberg wavelet set if every Gabor field over $I$ is a Parseval frame (mother-)wavelet for $L^2(\Bbb R^2)$. We then show that $I$ is a Heisenberg wavelet set if and only if $I$ is both translation congruent with a subset of the unit interval and dilation congruent with the Shannon set. | |
| dc.identifier | https://arxiv.org/abs/0903.4989 | |
| dc.identifier | http://arxiv.org/abs/0903.4989 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230592 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42C40, 22E45 | |
| dc.title | Gabor fields and wavelet sets for the Heisenberg group | |
| dc.type | text |