Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment
| dc.creator | Calixto, Manuel | |
| dc.creator | Guerrero, Julio | |
| dc.date | 2004-06-24 | |
| dc.date | 2006-12-15 | |
| dc.date.accessioned | 2026-07-07T07:35:18Z | |
| dc.date.available | 2026-07-07T07:35:18Z | |
| dc.description | We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square integrable (modulo a subgroup, possibly) representations of the group $SL(2,\mathbb{R})$. A general procedure for obtaining unitary representations of a group $G$ of affine transformations on a space of signals $L^2(X,dx)$ is described, relating carrier spaces $X$ to (first or higher-order) ``polarization subalgebras'' ${\cal P}_X$. We also provide explicit admissibility and continuous frame conditions for wavelets on $\mathbb S^1$ and discuss the Euclidean limit in terms of group contraction. | |
| dc.description | 32 pages, LaTeX, 1 figure. Final version published in ACHA | |
| dc.identifier | https://arxiv.org/abs/math-ph/0406057 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0406057 | |
| dc.identifier | Appl. Comput. Harmon. Anal. 21, 204-229 (2006) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120049 | |
| dc.subject | Mathematical Physics | |
| dc.title | Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment | |
| dc.type | text |