Weaving Riesz Bases
Functional Analysis
2024-11-15 v2 Classical Analysis and ODEs
Abstract
This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is both necessary and sufficient for vector reconstruction, which applies to Fourier matrices. Furthermore, we show that these characterizations are still valid in the infinite-dimensional case, for Riesz bases. Finally, we obtain several results for weaving Riesz bases of translations.
Cite
@article{arxiv.2404.02229,
title = {Weaving Riesz Bases},
author = {Carlos Cabrelli and Ursula Molter and Felipe Negreira},
journal= {arXiv preprint arXiv:2404.02229},
year = {2024}
}
Comments
15 pages, to appear Journal of Fourier Analysis and Applications