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

数学科学：Toeplitz 算子、它们的谱性质和相关函数代数

• 批准号: 8802659
• 负责人: Pamela Gorkin
• 金额: $ 3.18万
• 依托单位: Bucknell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802659&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Toeplitz; Operators; Their

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.

该项目是关于解析函数代数的数学研究，获得了本科院校研究奖的支持。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，它们具有非凡的性质，这些性质使它们的研究成为一个多世纪以来数学及其应用的基础。当它们聚集成巴拿赫空间和函数的巴拿赫代数时，它们就可以用抽象的现代方法来处理。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（解析函数相对于面积测度可平方积），并重点讨论两个这样的算子何时可交换的问题。