Multivariable Operator Theory

这笔拨款将研究与多变量算子理论有关的一些问题，多变量算子理论是算子理论的一部分，研究交换算子的有限集合以及它们之间的联系和相互作用的方式。这些技巧既是代数的，也是分析的，分析的主要工具是使用多变量的解析函数，而代数的工具来自矩阵代数。此外，PI还将与本科生进行几项协同活动。这项提议的重点是无限维希尔伯特空间上的有限算子集合。这项工作与数学分析的其他领域联系在一起，有着丰富的激动人心的历史。此外，PI还将与本科生开展几项协同活动。

This grant will work on a number of problems connected with multivariable operator theory, that part of operator theory that examines finite collections of commuting operators and the ways in which they are related and interact. The techniques are both algebraic and analytic, with the main tools from analysis being the use of analytic functions of several variables while the algebraic tools are from matrix algebra. In addition the PI will engage in several synergistic activities with undergraduates.The focus of this proposal is a finite collection of operators on a Hilbert space of infinite dimension. This work makes connections with other areas of mathematical analysis and has a rich history of excitement. In addition the PI will engage in several synergistic activities with undergraduates.