On weaving g-frames for Hilbert spaces

TL;DR

This paper introduces and analyzes the concept of weaving g-frames in Hilbert spaces, establishing properties, conditions, and perturbation results relevant for applications like sensor networks.

Contribution

It extends the theory of weaving frames to g-frames, providing necessary and sufficient conditions, and explores their stability and perturbation properties.

Findings

Weakly woven is equivalent to woven g-frames

Provided necessary conditions in terms of frame bounds

Presented Paley-Wiener-type perturbation results

Abstract

Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley-Wiener-type perturbation results for weaving g-frames.