- #1
nomadreid
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- Why is "ordered but not periodic structure" equivalent to "distribution where it and its Fourier transform both have discrete supports"?
https://en.wikipedia.org/wiki/Riemann_hypothesis#Quasicrystals a quasicrystal as "a distribution with discrete support whose Fourier transform also has discrete support."
https://en.wikipedia.org/wiki/Quasicrystal#Mathematicsdefines a quasicrystal as "a structure that is ordered but not periodic".
I would be grateful for an explanation of the equivalence between the two definitions. I read further down in the second article, in https://en.wikipedia.org/wiki/Quasicrystal#Mathematics where it gave an explanation which perhaps satisfies the better informed than me, without my seeing the connection, either formal or informal. Thanks.
https://en.wikipedia.org/wiki/Quasicrystal#Mathematicsdefines a quasicrystal as "a structure that is ordered but not periodic".
I would be grateful for an explanation of the equivalence between the two definitions. I read further down in the second article, in https://en.wikipedia.org/wiki/Quasicrystal#Mathematics where it gave an explanation which perhaps satisfies the better informed than me, without my seeing the connection, either formal or informal. Thanks.