Resumen de An example concerning Fourier analytic criteria for translational tiling

Nir Lev

• It is well known that the functions f∈L1(Rd) whose translates along a lattice ΛΛ 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 Λ⊂R (a small perturbation of the integers) for which no characterization of this kind is possible: there are two functions f,g∈L1(R) whose Fourier transforms have the same set of zeros, but such that +Λ is a tiling while g+Λ is not