Weighted Dirac combs with pure point diffraction
Weighted Dirac combs with pure point diffraction
复制标题
具有纯点衍射的加权狄拉克梳
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
R. Moody
中科院分区：
文献类型：
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作者：
M. Baake;R. Moody
研究了局部紧阿贝尔群上的一类平移有界复测度，其具有加权狄拉克梳的形式。给定这样的狄拉克梳，我们对它的衍射谱感兴趣，它作为自相关测量的傅里叶变换出现。我们提出了一组足够的条件来确保衍射测量是纯点测量。同时，我们建立了与剪切和投影形式主义以及几乎周期性测量理论的自然联系。我们的条件足够通用，足以涵盖已知的模型集理论，而且还包括诸如可见晶格点之类的示例。
A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simultaneously, we establish a natural link to the cut and project formalism and to the theory of almost periodic measures. Our conditions are general enough to cover the known theory of model sets, but also to include examples such as the visible lattice points.