Abstract
Fourier quasicrystals are tempered distributions μ which satisfy symmetric conditions on μ 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 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 μ on Rd whose Wigner transform, W(μ), is supported on a product of two uniformly discrete sets in Rd is a quasicrystal. This result is partially extended to a generalization of the Wigner transform, called matrix-Wigner transform which is defined in terms of the Wigner transform and a linear map T on R2.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
