Fourier uniqueness and non-uniqueness pairs
Classical Analysis and ODEs
2023-06-27 v1 Complex Variables
Abstract
Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a non-uniqueness pair for the Fourier transform. These conditions are close to each other. The uniqueness result can be upgraded to an interpolation formula, which in turn produces an abundance of discrete measures with discrete Fourier transform.
Cite
@article{arxiv.2306.14013,
title = {Fourier uniqueness and non-uniqueness pairs},
author = {Aleksei Kulikov and Fedor Nazarov and Mikhail Sodin},
journal= {arXiv preprint arXiv:2306.14013},
year = {2023}
}
Comments
53 pages