An example concerning Fourier analytic criteria for translational tiling
Nir Lev
Bar-Ilan University, Ramat-Gan, Israel
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Abstract
It is well known that the functions whose translates along a lattice form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a discrete set (a small perturbation of the integers) for which no characterization of this kind is possible: there are two functions whose Fourier transforms have the same set of zeros, but such that is a tiling while is not.
Cite this article
Nir Lev, An example concerning Fourier analytic criteria for translational tiling. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1975–1991
DOI 10.4171/RMI/1318