Diffraction of Weighted Lattice Subsets
Diffraction of Weighted Lattice Subsets
复制标题
加权晶格子集的衍射
DOI：
10.4153/cmb-2002-050-2
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Baake
中科院分区：
文献类型：
--
作者：
M. Baake
摘要在格$\Gamma$上支持的具有有界复权的欧氏空间中的点测度的Dirac梳继承了格结构的某些一般性质。特别是，它的自相关承认因式分解成一个连续的函数和uniformlattice狄拉克梳，其衍射措施是周期性的，与对偶格${{\Gamma }^{*}}$作为格的周期。这一陈述在拓扑具有可数基的局部紧阿贝尔群的情况下仍然成立。
Abstract A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice $\Gamma$ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniformlattice Dirac comb, and its diffraction measure is periodic, with the dual lattice ${{\Gamma }^{*}}$ as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.