On wovenness of K-fusion frames

TL;DR

This paper explores the properties of weaving K-fusion frames, a generalization of frames in Hilbert spaces, focusing on their characterizations, stability under perturbations, and applications in wireless sensor networks.

Contribution

It introduces the concept of weaving K-fusion frames, providing new characterizations and analyzing their stability and robustness in various spaces.

Findings

Characterizations of weaving K-fusion frames in different spaces

Perturbation stability results for weaving K-fusion frames

Conditions for erasure resilience of frame components

Abstract

In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. K-fusion frames come naturally (having significant applications) when one needs to reconstruct functions (signals) from a large data in the range of a bounded linear operator. Getting inspiration from the concept of weaving frames in Hilbert space, we study the weaving form of K-fusion frames which have significant applications in wireless sensor networks. This article produces various characterizations of weaving K-fusion frames in different spaces. Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize wovenness of the same.