2023/02/15 by Lawton, Wayne M., Tsikh, August K.
#32A27 #32A60 #52C23 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.07464
We derive sufficient conditions for an atomic measure ∑λ∈ Λ mλ δλ, where Λ⊂ \mathbb Rn, mλ are positive integers, and δλ is the point measure at λ, to be a Fourier quasicrystal, and suggest why they may also be necessary. These conditions extend the necessary and sufficient conditions derived by Lev, Olevskii, and Ulanovskii for n = 1. Our methods exploit the toric geometry relation between Grothendieck residues and Newton polytopes derived by Gelfond and Khovanskii.