Continuous action of Lie groups on $\mathbb{R}^n$ and Frames
| dc.creator | Olafsson, Gestur | |
| dc.date | 2003-04-23 | |
| dc.date.accessioned | 2026-07-07T04:57:17Z | |
| dc.date.available | 2026-07-07T04:57:17Z | |
| dc.description | Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. In this article we discuss the construction of frames for $L^2(\R^n)$ using the action of closed subgroups $H\subset \mathrm{GL}(n,\mathbb{R})$ such that $H$ has an open orbit $\cO$ in $\R^n$ under the action $(h,ω)\mapsto (h^{-1})^T(ω)$. If $H$ has the form $ANR$, where $A$ is simply connected and abelian, $N$ contains a co-compact discrete subgroup and $R$ is compact containing the stabilizer group of $ω\in\cO$ then we construct a frame for the space $L^2_{\cO}(\R^n)$ of $L^2$-functions whose Fourier transform is supported in $\cO$. We apply this to the case where $H^T=H$ and the stabilizer is a symmetric subgroup, a case discussed for the continuous wavelet transform in a paper by Fabec and Olafsson. | |
| dc.identifier | https://arxiv.org/abs/math/0304360 | |
| dc.identifier | http://arxiv.org/abs/math/0304360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67214 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42C40, 43A85 | |
| dc.title | Continuous action of Lie groups on $\mathbb{R}^n$ and Frames | |
| dc.type | text |