Mathematical Sciences: Functional Analysis and Function Theory

加内特教授的研究项目是函数论。 要研究的主题包括有界的代数 解析函数的单位圆盘，电晕问题， 平面、解析容量和拟共形映射。 加内特教授研究的主要焦点是理论 函数的一个复杂的变量是可微的， 初等微积分的意义。这些函数定义在 域在平面上，但不一定在其边界上。 一些 分析中最有趣的问题是关于 这些函数随着复变量接近边界而起作用。 加内特教授的研究将部分集中在这些问题上。

Professor Garnett's research project is in function theory. The topics to be investigated include the algebra of bounded analytic functions on the unit disk, the corona problem in the plane, analytic capacity, and quasiconformal mappings. The main focus of Professor Garnett's research is the theory of functions of one complex variable which are differentiable in the sense of elementary calculus. These functions are defined on a domain in the plane but not necessarily on its boundary. Some of the most interesting problems in analysis concern the behavior of these functions as the complex variable approaches the boundary. Professor Garnett's research will focus in part on such questions.