论文标题
动态系统的纯点光谱，平均周期性
Pure point spectrum for dynamical systems and mean almost periodicity
论文作者
论文摘要
我们考虑了局部紧凑，$σ$ compact Abelian群体上的可分离的千古拓扑动力学系统。我们通过在动力学系统点几乎具有周期性的合适概念来研究纯点频谱。更具体地说，我们通过普通点的平均周期性来表征纯点光谱。然后，我们继续展示besicovitch几乎是周期性的点如何决定本征函数和在这种情况下的度量。此后，我们表征了由Weyl几乎周期性点产生的那些系统，并用它来表征弱和玻璃薄饼几乎周期性的系统。最后，我们将应用程序申请按至十足的订单。
We consider metrizable ergodic topological dynamical systems over locally compact, $σ$-compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More specifically, we characterize pure point spectrum via mean almost periodicity of generic points. We then go on and show how Besicovitch almost periodic points determine both eigenfunctions and the measure in this case. After this, we characterize those systems arising from Weyl almost periodic points and use this to characterize weak and Bohr almost periodic systems. Finally, we consider applications to aperiodic order.
