Mathematical Sciences: Functional Analysis and Function Theory

加内特教授的研究项目是功能理论。研究的主题包括单位圆盘上有界解析函数的代数、平面上的电晕问题、解析能力和拟共形映射。加内特教授的主要研究重点是一元复变函数的理论，这些函数在初等微积分的意义上是可微的。这些函数在平面上的一个定义域上定义，但不一定在其边界上定义。分析中一些最有趣的问题涉及到当复变量接近边界时这些函数的行为。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.