The Dirac combs of primitive Pisot–Vijayaraghavan (PV) inflations on the real line or, more generally, in \({\mathbb {R}}^d\) are analysed. We construct a mean-orthogonal splitting for such Dirac combs that leads to the classic Eberlein decomposition on the level of the pair correlation measures, and thus to the separation of pure point versus continuous spectral components in the corresponding diffraction measures. This is illustrated with two guiding examples, and an extension to more general systems with randomness is outlined.

中文翻译：

---

光伏充气系统中的Eberlein分解

分析了原始Pisot-Vijayaraghavan（PV）实线或更普遍地在\（{\ mathbb {R}} ^ d \）中的狄拉克梳。我们为这种狄拉克梳子构造了均值-正交分裂，这导致在对相关度量水平上的经典Eberlein分解，从而在相应的衍射度量中分离了纯点对连续光谱分量。这通过两个指导示例进行说明，并概述了对具有随机性的更通用系统的扩展。