离散格的扰动与概周期集
Perturbations of discrete lattices and almost periodic sets
摘要：
$p$维欧氏空间中的离散集是{ \it概周期的}，如果在该集合的点处具有单位质量的测度在弱意义下是概周期的.我们建议构造正概周期离散集作为满秩离散格的概周期扰动。证明了实轴上的每个概周期离散集都是某个等差数列的概周期扰动。接下来，我们考虑符号几乎周期离散集，即，当质量为$\pm1$的带号测度在离散集的点上是概周期的时候.我们构造了一个非概周期的符号离散集，而相应的带号测度在分布意义下是概周期的。另外，我们构造了一个符号概周期离散集，使得在该集的所有点上质量为+1的测度不是概周期的。
英文摘要：
A discrete set in the $p$-dimensional Euclidian space is {\it almost periodic}, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We propose to construct positive almost periodic discrete sets as an almost periodic perturbation of a full rank discrete lattice. Also we prove that each almost periodic discrete set on the real axes is an almost periodic perturbation of some arithmetic progression. Next, we consider signed almost periodic discrete sets, i.e., when the signed measure with masses $\pm1$ at points of a discrete set is almost periodic. We construct a signed discrete set that is not almost periodic, while the corresponding signed measure is almost periodic in the sense of distributions. Also, we construct a signed almost periodic discrete set such that the measure with masses +1 at all points of the set is not almost periodic.
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