Mathematical Sciences: Toeplitz Operators and Hilbert Spaces of Analytic Functions

麦卡锡教授的研究项目将涵盖一些 希尔伯特空间算子理论和复分析领域：（a）他 我将把Toeplitz算子理论的某些方面扩展到 对数模代数的设定(b)他将调查 解析Hilbert空间上Toeplitz算子的有界性 功能协调发展的(c)他将研究有关Toeplitz的问题 多个复变量中的运算符。 希尔伯特空间算子本质上是无穷矩阵， 复数 这些运营商在各个领域都有应用 在应用科学和纯数学中的应用。 这种类型的 研究是试图将某些重要的家庭， 这样的物体。

Professor McCarthy's research project will cover a number of areas in Hilbert space operator theory and complex analysis: (a) He will extend some aspects of the theory of Toeplitz operators to the setting of logmodular algebras. (b) He will investigate the boundedness of Toeplitz operators on Hilbert spaces of analytic functions. (c) He will study questions dealing with Toeplitz operators in several complex variables. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important families of such objects.