On Excesses and Duality in Woven Frames
Abstract
Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven frames and prove that any two frames in a separable Hilbert space that are woven have the same excess. We also show that every frame with a large class of duals is woven provided that its redundant elements have small enough norm. Also, we try to transfer the woven property from frames to their duals and vise versa. Finally, we look at which perturbations of dual frames preserve the woven property, moreover it is shown that under some conditions the canonical Pareseval frame of two woven frames are also woven.
Cite
@article{arxiv.2101.00710,
title = {On Excesses and Duality in Woven Frames},
author = {Elahe Agheshteh Moghaddam and Ali Akbar Arefijamaal},
journal= {arXiv preprint arXiv:2101.00710},
year = {2021}
}
Comments
This article is containing 16 pages and it is published in journal of Bulletin of the Malaysian