Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778614 | Advances in Mathematics | 2017 | 26 Pages |
Abstract
We prove that a positive-definite measure in Rn with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent results where we proved this under the assumption that also the spectrum is uniformly discrete. As an application we obtain that Hof's quasicrystals with uniformly discrete diffraction spectra must have a periodic diffraction structure.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Nir Lev, Alexander Olevskii,