插值集与零序列
Interpolation sets and nilsequences
摘要：
为了对Frantzikinakis的一个问题给出肯定的回答，我们研究了$\mathbb{N}$的一类子集，称之为插值集，在这类子集上每个有界序列都可以扩张为$\mathbb{N}$上的概周期序列. Strzelecki证明了缺集是插值集。证明了比所有缺集都稠密的集不能是插值集。我们还扩展了概念的插值集的nilsequences和模拟Frantzikinakis的问题，任意序列是假的。
英文摘要：
To give positive answer to a question of Frantzikinakis, we study a class of subsets of $\mathbb{N}$, called interpolation sets, on which every bounded sequence can be extended to an almost periodic sequence on $\mathbb{N}$. Strzelecki has proved that lacunary sets are interpolation sets. We prove that sets that are denser than all lacunary sets cannot be interpolation sets. We also extend the notion of interpolation sets to nilsequences and show that the analogue to Frantzikinakis' question for arbitrary sequences is false.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
