论文标题
带有预发borel Windows的型号集
Model sets with precompact Borel windows
论文作者
论文摘要
鉴于剪切和项目方案和预熟练的borel窗口，我们表明，几乎所有窗户的位置几乎都会引起besicovitch几乎周期性的狄拉克梳子。特别是，所有这些位置导致纯点衍射点设置，由窗户的协变量和衍射为窗口傅立叶变换的平方给出的自相关。此外，存在傅立叶-BOHR系数，并且Bragg峰的强度由其绝对值平方给出。我们显示了具有纯点动力学频谱的千古量度的存在，因此所有这些窗口位置都会产生到点集，这对于此度量是一般的。我们通过重新加入最大密度的弱模型集的类别来完成论文。
Given a cut and project scheme and a pre-compact Borel window we show that almost surely all positions of the window give rise to point sets with Besicovitch almost periodic Dirac combs. In particular, all those positions lead to pure point diffractive point sets with autocorrelation given by the covariogram of the window and diffraction given by the square of the Fourier transform of the window. Moreover the Fourier--Bohr coefficients exist and the intensity of the Bragg peaks is given by their absolute value square. We show the existence of an ergodic measure with pure point dynamical spectrum such that all those window positions give rise to point sets which are generic for this measure. We complete the paper by reanalysing the class of weak model sets of maximal density.
