A new description of uniformly spread discrete sets

2025/10/13 by Dudko, A., Favorov, S.
#52C23 #52C35 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2510.11061

Abstract

We prove that each discrete set in the Euclidean space that has bounded changes under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laszkovich. In particular, the support of every Fourier quasicrystal with unit masses is uniformly spread.

Citations

• Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
• Non-negative crystalline and Poisson measures in the Euclidean space
• Generalized Fourier quasicrystals, almost periodic sets, and zeros of Dirichlet series
• Fourier quasicrystals with unit masses
• Almost periodic discrete sets
• A uniformly spread measure criterion

Related

• Temperate distributions with locally finite support and spectrum on Euclidean spaces
• Fourier quasicrystals and Lagarias' conjecture
• Large Fourier Quasicrystals and Wiener's Theorem
• Quasicrystals with discrete support and spectrum
• Fourier quasicrystals and distributions on Euclidean spaces with spectrum of bounded density