Wigner transform and quasicrystals

Fourier quasicrystals are tempered distributions μ which satisfy symmetric conditions on and μˆ. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In this paper we explore direction considering type representations instead separately distribution its transform. More precisely prove a Rd whose Wigner transform, W(μ), is supported product two uniformly discrete sets quasicrystal. result partially extended to generalization called matrix-Wigner transform defined terms linear map T R2.