论文标题
纯离散频谱和常规模型在r^d上的单模型替代瓷砖中设置
Pure Discrete Spectrum and Regular Model Sets in Unimodular Substitution Tilings on R^d
论文作者
论文摘要
我们考虑了r^d的原始替代瓷砖，其膨胀图是单模型的。我们假设膨胀图的所有特征值都是具有相同多重性的代数共轭物。在这种情况下，我们可以使用欧几里得内部空间构建一个切割和项目。在某些额外的条件下，我们表明，如果替换瓷砖具有纯离散频谱，那么相应的代表点集是该剪切和项目方案中的常规模型集。
We consider primitive substitution tilings on R^d whose expansion maps are unimodular. We assume that all the eigenvalues of the expansion maps are algebraic conjugates with the same multiplicity. In this case, we can construct a cut-and-project scheme with a Euclidean internal space. Under some additional condition, we show that if the substitution tiling has pure discrete spectrum, then the corresponding representative point sets are regular model sets in that cut-and-project scheme.
