English

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.

Keywords

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

R2 v1 2026-06-28T11:13:32.343Z