A short guide to pure point diffraction in cut-and-project sets
A short guide to pure point diffraction in cut-and-project sets
复制标题
切割和投影集中纯点衍射的简短指南
DOI：
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发表时间：
2016
期刊：
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通讯作者：
Nicolae Strungaru
中科院分区：
文献类型：
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作者：
C. Richard;Nicolae Strungaru
本文简要地回顾了准晶的衍射，然后给出了一个初等的替代证明的衍射公式的规则切割和投影集，这是基于Bochner定理从傅立叶分析。这澄清了一个普遍的观点，即准晶的衍射是由其基础晶格的衍射决定的。为了说明我们的方法，我们还将处理一些著名的显式可解的例子。
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner’s theorem from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.