2023/08/15 by Sergii Favorov, Favorov, Sergii
Materials Science · Mathematics · #42A38 #42A75 #52C23 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2308.07585
openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let μ be a positive measure on the real line with locally finite support Λ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire almost periodic function with a set of zeros Λ, taking multiplicities into account. A necessary and sufficient condition for the exponential growth of this function is also found. Our constructions are based on the properties of almost periodic sets on the line. In particular, in the article we find a simple representation of such sets.