Mathematical Sciences: Functional Analysis and Function Theory

加内特教授的研究项目是函数论。要研究的主题包括单位圆盘上有界解析函数的代数，平面上的冠状问题，解析能力，以及拟共形映射。加内特教授的主要研究重点是在初等微积分意义下可微的一元复变函数理论。这些函数定义在平面中的区域上，但不一定定义在其边界上。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.