Local-to-global frames and applications to dynamical sampling problem

Year: 2019

Type: preprint

Abstract: In this paper we consider systems of vectors in a Hilbert space $\mathcal{H}$ of the form $\{g_{jk}: j \in J, \, k\in K\}\subset \mathcal{H}$ where $J$ and $K$ are countable sets of indices. We find conditions under which the local reconstruction properties of such a system extend to global stable recovery properties on the whole space. As a particular case, we obtain new local-to-global results for systems of type $\{A^ng\}_{g\in\mathcal{G},0\leq n\leq L }$ arising in the dynamical sampling problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1909.02987

Authors: Aldroubi, Akram, Cabrelli, Carlos, Molter, Ursula, Petrosyan, Armenak

Institutions: Vanderbilt University, Universidad de Buenos Aires, Oak Ridge National Laboratory

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Battelle, UT-Battelle, Consejo Nacional de Investigaciones Científicas y Técnicas, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires, Oak Ridge National Laboratory

OpenAlex ID: W4288113237