Mathematical Sciences: Linear Fractional Models and Composition Operators

波登教授将研究 复平面单位圆盘的全纯映射 本身 该项目涉及寻找线性分数模型 这张地图有问题。 调查将在 解析Hilbert空间上的复合算子框架 功能协调发展的 这项工作的一个主要组成部分将涉及使用 一台电脑来生成图片， 分析。 该项目的一部分将与积极的 本科生的参与。 希尔伯特空间算子本质上是无限的 复数的矩阵 这些运营商有应用程序 在应用科学和纯数学的各个领域都是如此。 波登的研究试图理解某些重要的 这类物体的种类。

Professor Bourdon will investigate the iteration of holomorphic maps of the unit disk of the complex plane into itself. The project concerns finding a linear fractional model of the map in question. The investigation will take place in the framework of composition operators on a Hilbert space of analytic functions. A major component of the work will involve the use of a computer to generate conjectures and then prove them analytically. Part of the project will be done with the active participation of undergraduates. 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. Bourdon's research is an attempt to understand certain important classes of such objects.