正定离散强概周期测度与Bragg衍射
Positive Positive Definite Discrete Strong Almost Periodic Measures and Bragg Diffraction
摘要：
本文证明了正、正定、离散和强概周期测度锥$\PPD$具有一个有趣的性质：给定任意正、正定测度$μ$小于$\PPD$中的某个测度，则$μ$的强概周期部分$μ_S$也在$\PPD$中.然后，我们使用这个结果来证明，给定一个正加权梳$ω$有限的局部复杂性和纯点衍射，任何正梳小于$ω$有平凡的布拉格谱或一个相对密集的布拉格峰。
英文摘要：
In this paper we prove that the cone $\PPD$ of positive, positive definite, discrete and strong almost periodic measures has an interesting property: given any positive and positive definite measure $μ$ smaller than some measure in $\PPD$, then the strong almost periodic part $μ_S$ of $μ$ is also in $\PPD$. We then use this result to prove that given a positive weighted comb $ω$ with finite local complexity and pure point diffraction, any positive comb less than $ω$ has either trivial Bragg spectrum or a relatively dense set of Bragg peaks.
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