Almost periodic distributions and crystalline measures

2022/11/30 by Sergii Favorov, Favorov, Sergii
Materials Science · Mathematics · #46F12 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2211.16856

openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the properties of distributions and measures with discrete support, we investigate temperate almost periodic distributions on the Euclidean space and connection with their Fourier transforms. We also study relations between the Fourier transform of almost periodic distributions and their Fourier coefficients. The main result of the article is the construction of a crystalline measure on the real line, which is neither almost periodic distribution, nor a Fourier quasicrystal.

Related

• Generalized Fourier quasicrystals and almost periodic sets
• Non-negative crystalline and Poisson measures in the Euclidean space
• Temperate distributions with locally finite support and spectrum on Euclidean spaces
• Fourier quasicrystals and distributions on Euclidean spaces with spectrum of bounded density
• The crystalline measure that is not a Fourier Quasicrystal