当前位置: X-MOL 学术J. Math. Anal. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Discrete frames for L2(Rn2) arising from tiling systems on GLn(R)
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-05-14 , DOI: 10.1016/j.jmaa.2021.125328
Mahya Ghandehari , Kris Hollingsworth

A discrete frame for L2(Rd) is a countable sequence {ej}jJ in L2(Rd) together with real constants 0<AB< such thatAf22jJ|f,ej|2Bf22, for all fL2(Rd). We present a method of sampling continuous frames, which arise from square-integrable representations of affine-type groups, to create discrete frames for high-dimensional signals. Our method relies on partitioning the ambient space by using a suitable “tiling system”. We provide all relevant details for constructions in the case of Mn(R)GLn(R), although the methods discussed here are general and could be adapted to some other settings. Finally, we prove significantly improved frame bounds over the previously known construction for the case of n=2.



中文翻译:

离散框架 大号2个[Rñ2个 产生于 GLñ[R

离散框架 大号2个[Rd 是一个可数的序列 {ËĴ}ĴĴ大号2个[Rd 连同实常数 0<一种< 这样一种F2个2个ĴĴ|FËĴ|2个F2个2个 对所有人 F大号2个[Rd。我们提出了一种对连续帧进行采样的方法,该方法是从仿射类型组的平方可积表示中产生的,以创建用于高维信号的离散帧。我们的方法依赖于通过使用合适的“平铺系统”对环境空间进行分区。如果发生以下情况,我们会提供与施工有关的所有详细信息:中号ñ[RGLñ[R,尽管此处讨论的方法是通用的,并且可以适用于其他一些设置。最后,对于以下情况,我们证明比以前已知的结构显着改善了框架边界ñ=2个

更新日期:2021-05-24
down
wechat
bug