标题： 准晶与几乎周期性 显示英文标题

标题： Quasicrystals and almost periodicity

摘要： 我们引入了一个拓扑结构${\cal T}$，定义在欧几里得空间中一致离散子集的空间$U$上。 假设$S$在$U$中唯一存在自相关测度。 $S$的衍射测度是纯粹原子的当且仅当$S$在$(U,{\cal T})$中几乎是周期性的。 这一结果将理想的准晶体与几乎周期性联系起来。 在遍历点过程的背景下，自相关测度是已知存在的。 然后，衍射测度是纯粹原子的当且仅当动力系统具有纯点谱。 作为示例，我们研究了变形模型集。 显示英文摘要

摘要： We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is almost periodic in $(U,{\cal T})$. This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to exist. Then, the diffraction measure is purely atomic if and only if the dynamical system has a pure point spectrum. As an illustration, we study deformed model sets.