Fourier quasicrystals and distributions on Euclidean spaces with spectrum of bounded density

2022/03/13 by Sergii Favorov, Favorov, Sergii
Materials Science · Mathematics · #46F10 (primary) 42B10 #52C23 (secondary) #Analytic and geometric function theory #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2203.06733

openalex publication_date 2022/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice Dirac combs. These theorems are derived from properties of families of discretely supported measures and almost periodic distributions.

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