发表机构
Northern Illinois University; Université Laval（北伊利诺伊大学; 拉瓦尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究多圆盘Hardy空间上乘子联合轨道的闭张成，证明符号数少于维数时余维数无限，并给出两个初等证明及双圆盘上的精确余维数界。
AI 中文摘要
我们研究了多圆盘Hardy空间$H^2(\mathbb D^d)$上全纯乘子的有限个联合轨道的闭张成。如果使用的符号少于$d$个，则每个这样的张成具有无限余维数。符号可以无界，前提是所有轨道向量都属于Hardy空间。我们给出两个初等证明。第一个使用公共水平集和独立点赋值；对于有界符号，这些赋值产生联合伴随特征向量。第二个使用有限Taylor截面和截断卷积（也称为Jury积）的幂零结构。对于$r$个生成元和$q<d$个符号，边长为$n$的立方体上的轨道维数为$O(n^q)$，而环境维数为$n^d$。在双圆盘上，我们得到显式余维数界$MN-r(M+N-1)$，该界对单个轨道是精确的。坐标乘子达到参数阈值。我们还解释了这些障碍如何与核插值以及模型空间上压缩移位对动力框架的既有表示相关联。
英文摘要
We study the closed spans of finitely many joint orbits of holomorphic multipliers on the Hardy space $H^2(\mathbb D^d)$ of the polydisk. If fewer than $d$ symbols are used, every such span has infinite codimension. The symbols may be unbounded, provided that all orbit vectors belong to the Hardy space. We give two elementary proofs. The first uses common level sets and independent point evaluations; for bounded symbols, these evaluations yield joint adjoint eigenvectors. The second uses finite Taylor sections and the nilpotent structure of truncated convolution, also known as the Jury product. For $r$ generators and $q<d$ symbols, the orbit dimension on a cube of side $n$ is $O(n^q)$, whereas the ambient dimension is $n^d$. In the bidisk we obtain the explicit codimension bound $MN-r(M+N-1)$, which is sharp for a single orbit. The coordinate multipliers attain the parameter threshold. We also explain how these obstructions relate to kernel interpolation and the established representation of dynamical frames by compressed shifts on model spaces.
Comments11 pages
