从有限维到无限维全矩问题的拟解析性和决定性
Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
摘要：
本文旨在说明拟解析函数理论在研究有限维和无限维空间上矩量问题的决定性中所起的重要作用。特别是，准解析准则的自伴的运营商和他们的交换性是至关重要的，以确定是否或不一个措施是唯一确定的时刻。我们的主要目标是指出，这是一个共同的特点，在有限维和无限维矩问题的确定性问题，通过审查一些最知名的确定性结果从这个角度来看。我们还收集了一些性质的独立利益有关的拟解析类的特性与日志凸序列。
英文摘要：
This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.
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。
