Analysis in Spaces of Analytic Functions

解析函数空间中的分析

• 批准号: 9705207
• 负责人: Dechao Zheng
• 金额: $ 6.18万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9705207&HistoricalAwards=false
• 关键词: Analysis; Spaces; Analytic; Functions

Abstract Zheng Zheng will conduct research on problems arising from the interaction between complex function theory and functional analysis. Primary emphasis will rest on the study of certain important spaces of analytic functions and operators on these spaces. The topics to be considered include the Hilbert transform, the Berezin transform, algebras on the unit disk, Toeplitz operators, Hankel operators, and Bergman spaces. This project focuses on a central problem in the theory of Toeplitz operators and Hankel operators, which is to establish relationships between the fundamental properties of those operators and analytic and geometric properties of their symbols. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. It has its origins in mathematical physics, in particular, in the study of quantum mechanics. The modeling of the atom required the development of non-commutative analysis. The commutator of operators is the measure of non-commutativity. A good portion of this project deals with operators and the analysis of their commutators that acting on spaces of analytic functions.

郑铮将对复函数理论与泛函分析相互作用所产生的问题进行研究。主要的重点将放在研究解析函数的某些重要空间和这些空间上的算子。要考虑的主题包括Hilbert变换、Berezin变换、单位盘上的代数、Toeplitz算子、Hankel算子和Bergman空间。本课题主要研究Toeplitz算子和Hankel算子理论中的一个中心问题，即建立Toeplitz算子的基本性质与其符号的解析性质和几何性质之间的关系。算符理论是研究矩阵的无限维推广的数学部分。它起源于数学物理学，特别是量子力学的研究。原子的建模需要非交换分析的发展。算子的对易子是非对易性的度量。这个项目的很大一部分涉及算子及其对解析函数空间上的对易子的分析。