Mathematical Sciences: Toeplitz Operators, Their Spectral Properties and Related Function Algebras

这个项目得到了本科生研究机构奖的支持，是关于解析函数的代数的数学研究。这些函数可以被认为是某个非常简单的偏微分方程组的解，它们具有显著的性质，使它们的研究成为数学及其应用的基础长达一个多世纪。当它们被聚集到函数的Banach空间和Banach代数中时，它们变得易于用抽象的、现代的方法处理。更具体地说，Gorkin教授将研究包含所有有界解析函数的圆盘上有界函数的代数。她还将考虑具有有界符号的Toeplitz算子作用于圆盘的Bergman空间(解析函数关于面积度量平方可积)，重点是两个这样的算子何时可交换的问题。

This project, which is supported by a Research in Undergraduate Institutions award, is mathematical research on algebras of analytic functions. These functions, which may be thought of as the solutions of a certain very simple system of partial differential equations, enjoy remarkable properties that have made their study fundamental to mathematics and its applications for well over a century. When they are aggregated into Banach spaces and Banach algebras of functions, they become amenable to treatment by abstract, modern methods. More specifically, Professor Gorkin will investigate algebras of bounded functions on the disk that contain all the bounded analytic functions. She will also consider Toeplitz operators with bounded symbol acting on the Bergman space of the disc (analytic functions square-integrable with respect to area measure), with emphasis on the question of when two such commute.