Multivariable Operator Theory

该基金将研究与多变量算子理论相关的一些问题，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相互关联和相互作用的方式。这些技术既有代数的，也有解析的，分析的主要工具是使用多变量解析函数，而代数的工具是来自矩阵代数。此外，PI将与本科生进行一些协同活动。这一建议的重点是无限维希尔伯特空间上算子的有限集合。这项工作与数学分析的其他领域建立了联系，并且有着丰富的兴奋历史。此外，PI将与本科生进行一些协同活动。

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.