Abstract

Frames play significant role as redundant building blocks in distributed signal processing. Getting inspirations from this concept, Bemrose et al. produced the notion of weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving \(K\)-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator \(K\). This article presents a flavor of weaving multiframelets. Various properties of weaving multiframelets are explored in the \(p\)-adic number field. Furthermore, several characterizations of \(p\)-adic weaving multiframelets have been analyzed.

中文翻译：

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$$p$$ -Adic 编织多框架

摘要

帧作为分布式信号处理中的冗余构建块发挥着重要作用。Bemrose 等人从这个概念中获得灵感。提出了希尔伯特空间中编织框架的概念。编织帧在传感器网络中具有有用的应用，同样，编织\(K\)帧已被证明在有界线性算子\(K\)范围内的信号重建过程中是有用的。本文介绍了编织多框架的风格。在\(p\) -adic 数域中探索了编织多框架的各种属性。此外，还分析了\(p\) -adic 编织多框架的几个特征。