Characterizations of weaving $K$-frames

Abstract

In distributed signal processing frames play significant role as redundant building blocks. Bemrose et al. were motivated from this concept, as a result they introduced 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 focuses on study, characterization of weaving $K$-frames in different spaces. Paley-Wiener type perturbations and conditions on erasure of frame components have been assembled to scrutinize woven-ness of $K$-frames.