Fourier quasicrystals with unit masses

TL;DR

This paper establishes that Fourier quasicrystals with unit masses are precisely the zero sets of exponential polynomials with imaginary frequencies, linking their structure to a specific class of entire functions.

Contribution

It proves that any Fourier quasicrystal with unit masses corresponds exactly to the zero set of an exponential polynomial with imaginary frequencies.

Findings

Fourier quasicrystals with unit masses are zero sets of exponential polynomials.

The structure of these quasicrystals is characterized by entire functions with imaginary frequencies.

This links the geometric configuration of quasicrystals to algebraic properties of exponential polynomials.

Abstract

Every set $\Lambda\subset R$ such that the sum of $\delta$-measures sitting at the points of $\Lambda$ is a Fourier quasicrystal, is the zero set of an exponential polynomial with imaginary frequencies.