Diffraction from visible lattice points and kth power free integers
Diffraction from visible lattice points and kth power free integers
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DOI：
10.1016/s0012-365x(99)00384-2
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发表时间：
2000-06-28
影响因子：
0.8
通讯作者：
Pleasants, PAB
中科院分区：
文献类型：
--
作者：
Baake, M;Moody, RV;Pleasants, PAB
我们证明了任意维数n大于或等于2的晶格的可见点集合都具有纯点衍射谱，并明确地确定了衍射谱。这解决了之前关于这种情况下衍射的确切性质的猜测。使用类似的方法，我们对 k 大于或等于 2 的 k 次幂整数的一维集合显示了相同的结果。特别有趣的是，这些集合都不是 Delone 集合 - 每个集合都有半径无界的孔。我们对无限点集衍射研究背后的数学思想进行了仔细的表述。 (C) 2000 Elsevier Science B.V. 保留所有权利。
We prove that the set of visible points of any lattice of dimension n greater than or equal to 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation. Using similar methods we show the same result for the one-dimensional set of kth-power-free integers with k greater than or equal to 2. Of special interest is the fact that neither of these sets is a Delone set - each has holes of unbounded inradius. We provide a careful formulation of the mathematical ideas underlying the study of diffraction from infinite point sets. (C) 2000 Elsevier Science B.V. All rights reserved.