Localized frames without inequalities
Functional Analysis
2025-06-12 v2
Abstract
We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the frame property and nine conditions that do not involve any inequalities. This is done by studying the properties of their frame-related operators on the co-orbit spaces generated by the reference Riesz basis. We apply our main result to the setting of shift-invariant spaces and obtain new conditions for stable sets of sampling.
Cite
@article{arxiv.2506.02862,
title = {Localized frames without inequalities},
author = {Peter Balazs and Lukas Köhldorfer and Michael Speckbacher},
journal= {arXiv preprint arXiv:2506.02862},
year = {2025}
}