Toral algebraic sets and function theory on polydisks
Toral algebraic sets and function theory on polydisks
复制标题
多圆盘上的托拉代数集和函数论
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. Stankus
中科院分区：
文献类型：
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作者：
J. Agler;John E. McCarthy;M. Stankus
一个环面代数集A是一个代数集，它与Tn的交足够大，可以确定A上的全纯函数。我们发展了这些集的理论，并给出了一些应用程序的函数理论在几个变量和运营商理论模型理论。特别是，我们表明，唯一性集的极值挑选问题的bidisk是一个toral代数集，合理的内部功能有零集的不可约组件是不是toral，和模型理论的交换对收缩有限缺陷的生活自然的toral代数集。
A toral algebraic set A is an algebraic set in ℂnwhose intersection with Tnis sufficiently large to determine the holomorphic functions on A. We develop the theory of these sets, and give a number of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite defect lives naturally on a toral algebraic set.