On weakly almost periodic measures
On weakly almost periodic measures
复制标题
关于弱几乎周期性的措施
DOI：
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发表时间：
2016
影响因子：
1.3
通讯作者：
Nicolae Strungaru
中科院分区：
文献类型：
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作者：
D. Lenz;Nicolae Strungaru
研究了平移有界弱概周期测度的衍射和动力学性质。证明了弱概周期测度的动力学船体是一个弱概周期动力系统，其极小分支由测度的强概周期分支的船体给出.特别地，船体是极小的当且仅当测度是强概周期的，并且船体总是可测地共轭到环面，并且具有连续特征函数的纯点谱。作为应用，我们证明了具有Meyer集或FLC支集的加权Dirac梳的稳定性，并证明了这类测度分别具有平凡或大纯点连续谱。我们通过研究两个弱概周期测度的Eberlein卷积来补充这些结果。在这里，我们证明了它是唯一的，是一个强概周期测度。最后，我们研究了弱概周期测度的Fourier-Bohr系数。
We study the diffraction and dynamical properties of translation bounded weakly almost periodic measures. We prove that the dynamical hull of a weakly almost periodic measure is a weakly almost periodic dynamical system with unique minimal component given by the hull of the strongly almost periodic component of the measure. In particular the hull is minimal if and only if the measure is strongly almost periodic and the hull is always measurably conjugate to a torus and has pure point spectrum with continuous eigenfunctions. As an application we show the stability of the class of weighted Dirac combs with Meyer set or FLC support and deduce that such measures have either trivial or large pure point respectively continuous spectrum. We complement these results by investigating the Eberlein convolution of two weakly almost periodic measures. Here, we show that it is unique and a strongly almost periodic measure. We conclude by studying the Fourier-Bohr coefficients of weakly almost periodic measures.
DOI：
10.1524/zkri.2008.1043
发表时间：
2008
期刊：
Zeitschrift für Kristallographie
影响因子：
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作者：
Grimm U
通讯作者：
Grimm U