arXivDaily arXiv每日学术速递 周一至周五更新
arXiv math-ph/0510053math-phmath.FAmath.MP
收藏

广义Weyl-Heisenberg群的Gabor型框架

Gabor-type Frames from Generalized Weyl-Heisenberg Groups

G. Honnouvo, S. Twareque Ali

备注：
22 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文提出了一种基于广义Weyl-Heisenberg群的Gabor型框架的构造方法。这些后者是通过中心扩展的群体，这是直接产品的局部紧阿贝尔群和他们的south。我们的结果推广了许多结果，出现在文献中，建立了标准魏尔-海森堡群的薛定谔表示的框架。特别是，我们得到了一个推广的结果在\cite{PO}，其中产品$ab$确定是否有可能的Gabor系统$\{E_{mb}T_{na}g \}_{m,n\in \mathbb Z}$是一个帧的$L^2(\mathbb R)$。作为一个特殊的例子的理论，我们研究的情况下，广义Weyl-Heisenberg群建成的$d$维环面。在同样的精神，我们也构造广义平移不变系统。

英文摘要：

We present in this paper a construction for Gabor-type frames built out of generalized Weyl-Heisenberg groups. These latter are obtained via central extensions of groups which are direct products of locally compact abelian groups and their duals. Our results generalize many of the results, appearing in the literature, on frames built out of the Schrödinger representation of the standard Weyl-Heisenberg group. In particular, we obtain a generalization of the result in \cite{PO}, in which the product $ab$ determines whether it is possible for the Gabor system $\{E_{mb}T_{na}g \}_{m,n\in \mathbb Z}$ to be a frame for $L^2(\mathbb R)$. As a particular example of the theory, we study in some detail the case of the generalized Weyl-Heisenberg group built out of the $d$-dimensional torus. In the same spirit we also construct generalized shift-invariant systems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑