"Wigner transform and quasicrystals"Boggiatto, PaoloFourier quasicrystals are tempered distributions which satisfy symmetric conditions on the distrubution itself and its Fourier transform. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In this talk we present recent results in this direction considering quasicrystals type conditions on time-frequency representations instead of separately on the distribution and its Fourier transform. More precisely we prove that a tempered distribution whose Wigner transform is supported on a product of two uniformly discrete sets is a quasicrystal. Furthermore we present some extensions of this result to matrix-Wigner transforms, which include most of the commonly used time-frequency representations. |
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