Frames of translates for model sets
Functional Analysis
2019-02-21 v3 Operator Algebras
Abstract
We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection between model sets and almost periodic functions and rely strongly on a Poisson summations formula for model sets to introduce the so-called bracket product, which then plays a crucial role in our approach. As a corollary to our main results we obtain a density statement for semi-regular Gabor frames.
Keywords
Cite
@article{arxiv.1801.05213,
title = {Frames of translates for model sets},
author = {Ewa Matusiak},
journal= {arXiv preprint arXiv:1801.05213},
year = {2019}
}