Multivariable Operator Theory

该资助将致力于解决与多变量算子理论相关的许多问题，该理论是算子理论的一部分，旨在研究交换算子的有限集合以及它们之间的相关和相互作用方式。 这些技术都是代数和分析，与主要工具，从分析是使用解析函数的几个变量，而代数工具是从矩阵代数。 此外，PI还将与本科生开展多项协同活动。本计划的重点是无限维希尔伯特空间上的有限算子集合。 这项工作使连接与其他领域的数学分析，并有丰富的历史兴奋。 此外，PI还将与本科生开展多项协同活动。

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.