关于Meyer集的Bragg衍射谱
On the Bragg Diffraction Spectra of a Meyer Set
摘要：
迈耶集具有相对密集的布拉格峰，因此它们可以被认为是（非周期性）晶体的基本数学示例。本文对Meyer集衍射的纯点部分作了较详细的研究。结果有两种。首先，我们表明，给定一个迈耶集和任何强度小于其布拉格峰的最大强度，一组布拉格峰的强度超过本身是迈耶集（在傅立叶空间）。第二，我们表明，如果迈耶集是修改通过添加和删除点，以这样一种方式，其密度是不改变太多（允许量被明确地作为原始密度的比例），然后新获得的一组仍然有一个相对密集的布拉格峰。
英文摘要：
Meyer sets have a relatively dense set of Bragg peaks and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in more detail. The results are of two kinds. First we show that given a Meyer set and any intensity a less than the maximum intensity of its Bragg peaks, the set of Bragg peaks whose intensity exceeds a is itself a Meyer set (in the Fourier space). Second we show that if a Meyer set is modified by addition and removal of points in such a way that its density is not altered too much (the allowable amount being given explicitly as a proportion of the original density) then the newly obtained set still has a relatively dense set of Bragg peaks.
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