论文标题
关于编织通用框架和广义的Riesz基地
On Weaving Generalized Frames and Generalized Riesz Bases
论文作者
论文摘要
编织框架在无线传感器网络中具有潜在的应用，这些网络需要在不同帧下进行信号的分布处理。在本文中，我们研究了编织通用框架（或$ g $ frames）和编织通用的正常基础（或$ g $ - 正式基础）的一些新属性。结果表明，$ g $ frame及其双$ g $ -frame是编织的。研究了最佳$ G $ -FRAGE界限和最佳通用$ G $ -FRAGE边界的相互关联。此外，我们提出了编织$ g $ frames的特征。给出了插图，以显示编织通用的Riesz底座和编织Riesz基地的性质差异。
Weaving frames have potential applications in wireless sensor networks that require distributed processing of signal under different frames. In this paper, we study some new properties of weaving generalized frames (or $g$-frames) and weaving generalized orthonormal bases (or $g$-orthonormal bases). It is shown that a $g$-frame and its dual $g$-frame are woven. The inter-relation of optimal $g$-frame bounds and optimal universal $g$-frame bounds is studied. Further, we present a characterization of weaving $g$-frames. Illustrations are given to show the difference in properties of weaving generalized Riesz bases and weaving Riesz bases.
