Fourier quasicrystals and Lagarias' conjecture (Q2809207)
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scientific article; zbMATH DE number 6586356
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier quasicrystals and Lagarias' conjecture |
scientific article; zbMATH DE number 6586356 |
Statements
27 May 2016
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quasicrystals
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Fourier transform
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Lagarias' conjecture
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unbounded measure
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temperate distribution
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almost periodic measure
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full-rank lattice
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0.89029706
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0.88774616
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0.88768315
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0.88473284
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0.88347423
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Fourier quasicrystals and Lagarias' conjecture (English)
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From author's abstract: ``\textit{J. C. Lagarias} [CRM Monogr. Ser. 13, 61--93 (2000; Zbl 1161.52312)] conjectured that if \(\mu\) is a complex measure on the \(p\)-dimensional Euclidean space with a uniformly discrete support and its Fourier transform in the sense of distributions is also a measure with a uniformly discrete support, then the support of \(\mu\) is a subset of a finite union of translates of some full-rank lattice. The conjecture was proved by \textit{N. Lev} and \textit{A. Olevskii} [Invent. Math. 200, No. 2, 585--606 (2015; Zbl 1402.28002)] in the case \(p = 1\). In the case of an arbitrary \(p\), they proved the conjecture for a positive measure \(\mu\).''NEWLINENEWLINENEWLINEIn the paper under review, the author considers similar problems for some cases of non-positive measures.
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