论文标题
分段可伸缩帧
Piecewise scalable frames
论文作者
论文摘要
在本文中，我们定义“分段可伸缩帧”。这个新的缩放过程使我们可以将许多帧更改为parseval框架，而这是先前的标准缩放。我们提供了必要和足够的条件，以使框架可扩展。我们表明，分段可伸缩性保留在统一转换下。与标准缩放不同，我们证明了$ \ rr^2 $和$ \ rr^3 $中的所有帧均可扩展。我们还表明，如果帧向量彼此靠近，那么它们可能无法分段可扩展。还提供了缩放常数的几种属性。
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to be piecewise scalable. We show that piecewise scalability is preserved under unitary transformations. Unlike standard scaling, we show that all frames in $\RR^2$ and $\RR^3$ are piecewise scalable. We also show that if the frame vectors are close to each other, then they might not be piecewise scalable. Several properties of scaling constants are also presented.
