单圈有向图上无界复合算子的次正规性：奇异例子
Subnormality of unbounded composition operators over one-circuit directed graphs: exotic examples
摘要：
最近的一个例子，一个非亚正规内射合成算子在一个$L^2$ -空间生成Stieltjes矩序列，本作者发明的三个，是建立在一个非局部有限的有向树。本文的主要目标是解决局部有限有向图上是否存在这样的算子的问题，并在肯定的情况下，找到具有这些性质的最简单的可能图（简单性指的是局部价）。对于局部有限有向图$\mathscr G_{2,0}$，该图由两个分支和一个环组成，该问题得到了肯定的解决。唯一的简单的有向图的问题仍然没有得到解决，由一个分支和一个循环。在$\mathscr G_{2,0}$框架下，深入研究了无界复合算子次正规性的唯一有效工具--相容性条件，给出了一种构造性的求解方法.该方法本身是部分基于转换Krein和Friedrichs措施来自移动Al-Salam-Carlitz $q$ -多项式或从四次生灭过程。
英文摘要：
A recent example of a non-hyponormal injective composition operator in an $L^2$-space generating Stieltjes moment sequences, invented by three of the present authors, was built over a non-locally finite directed tree. The main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and, in the affirmative case, to find the simplest possible graph with these properties (simplicity refers to local valency). The problem is solved affirmatively for the locally finite directed graph $\mathscr G_{2,0}$, which consists of two branches and one loop. The only simpler directed graph for which the problem remains unsolved consists of one branch and one loop. The consistency condition, the only efficient tool for verifying subnormality of unbounded composition operators, is intensively studied in the context of $\mathscr G_{2,0}$, which leads to a constructive method of solving the problem. The method itself is partly based on transforming the Krein and the Friedrichs measures coming either from shifted Al-Salam-Carlitz $q$-polynomials or from a quartic birth and death process.
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。
