Weyl-Heisenberg Frame Wavelets with Basic Supports

Simple item page
dc.creatorGuo, Xunxiang
dc.creatorDiao, Yuanan
dc.creatorDai, Xingde
dc.date2005-07-29
dc.date.accessioned2026-07-07T05:22:06Z
dc.date.available2026-07-07T05:22:06Z
dc.descriptionLet $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=χ_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by $b$ and translates by $a$, i.e., $\{e^{imbt}g(t-na\}_{m,n\in\mathbb{Z}}$ is a frame for $L^2(\mathbb{R})$. It is an open question on how to characterize all frame sets for a given pair $(a,b)$ in general. In the case that $a=2π$ and $b=1$, a result due to Casazza and Kalton shows that the condition that the set $F=\bigcup_{j=1}^{k}([0,2π)+2n_{j}π)$ (where $\{n_{1}<n_{2}<...<n_{k}\}$ are integers) is a Weyl-Heisenberg frame set for $(2π,1)$ is equivalent to the condition that the polynomial $f(z)=\sum_{j=1}^{k}z^{n_{j}}$ does not have any unit roots in the complex plane. In this paper, we show that this result can be generalized to a class of more general measurable sets (called basic support sets) and to set theoretical functions and continuous functions defined on such sets.
dc.description11 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0507609
dc.identifierhttp://arxiv.org/abs/math/0507609
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75934
dc.subjectFunctional Analysis
dc.subject42C99
dc.titleWeyl-Heisenberg Frame Wavelets with Basic Supports
dc.typetext

Files

Collections

arXiv