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arXiv · 2302.07464

Multidimensional Fourier Quasicrystals I. Sufficient Conditions

Wayne M. Lawton·August K. Tsikh
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Abstract

We derive sufficient conditions for an atomic measure $\sum_{\lambda \in \Lambda} m_\lambda\, \delta_\lambda,$ where $\Lambda \subset \mathbb R^n,$ $m_\lambda$ are positive integers, and $\delta_\lambda$ is the point measure at $\lambda,$ 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.

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Wayne M. Lawton, August K. Tsikh. 2023-02-15. Multidimensional Fourier Quasicrystals I. Sufficient Conditions. https://arxiv.org/abs/2302.07464

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