复矩问题：确定性与可拓性
The complex moment problem: determinacy and extendibility
摘要：
复矩序列就是在上对角半平面的整格点上允许正定扩张的序列。本文证明了在复矩序列是确定的且其唯一表示测度在$0$上没有原子的条件下，上述扩张是唯一的。转换关系的问题是作为一个开放的问题。当平面代数曲线与通过$0$的每一条直线的交线至多为一个点集时，至少有一个表示测度被支持，则建立了该问题的部分解.进一步的研究涉及代表措施的支持是Zagliki密集的$\mathbb C$以及复杂的时刻序列是恒定的一个家庭的平行“丢番图线”。所有这一切都得到了一堆说明性例子的支持。
英文摘要：
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom at $0$. The question of converting the relation is posed as an open problem. A partial solution to this problem is established when at least one of representing measures is supported in a plane algebraic curve whose intersection with every straight line passing through $0$ is at most one point set. Further study concerns representing measures whose supports are Zariski dense in $\mathbb C$ as well as complex moment sequences which are constant on a family of parallel "Diophantine lines". All this is supported by a bunch of illustrative examples.
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。
