Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Wigner transform and quasicrystals"

Boggiatto, Paolo

Fourier 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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