We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets of exponential polynomials with imaginary frequencies. This result is the special case of a general result on measures whose supports correspond to zero sets of absolutely convergent Dirichlet series with bounded spectrum.
On inversion of absolutely convergent weighted Dirichlet series in two variables
Fourier quasicrystals and distributions on Euclidean spaces with spectrum of bounded density
Generalized Fourier quasicrystals, almost periodic sets, and zeros of Dirichlet series
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