Bohr和Besicovitch概周期离散集与准晶
Bohr and Besicovitch almost periodic discrete sets and quasicrystals
摘要：
欧氏空间中的离散集$A$是概周期的，如果在集合的点处单位质量的测度是弱概周期的.我们调查的情况下，当$A-A$是离散的这样的集合的属性。特别地，如果$A$是Bohr概周期集，我们证明了$A$是某一满秩格的有限个平移的并.如果$A$是Besicovitch概周期集，则存在满秩格，使得在大多数情况下，它的平移与$A$的非空交是大的.
英文摘要：
A discrete set $A$ in the Euclidian space is almost periodic if the measure with the unite masses at points of the set is almost periodic in the weak sense. We investigate properties of such sets in the case when $A-A$ is discrete. In particular, if $A$ is a Bohr almost periodic set, we prove that $A$ is a union of a finite number of translates of a certain full--rank lattice. If $A$ is a Besicovitch almost periodic set, then there exists a full-rank lattice such that in most cases a nonempty intersection of its translate with $A$ is large.
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