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 is a countable sequence in together with real constants such that for all . 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 , 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 .
中文翻译:
离散框架 产生于
离散框架 是一个可数的序列 在 连同实常数 这样 对所有人 。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:,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。