Mathematical Sciences: Subnormal Operators and Banach Spaces of Holomorphic Functions

数学科学：次正规算子和全纯函数的 Banach 空间

• 批准号: 9531917
• 负责人: Liming Yang
• 金额: $ 3.81万
• 依托单位: University of Hawaii
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9531917&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Subnormal; Operators; Banach

Abstract of the project (item C) The principal investigator will continue to study the internal structure theory of subnormal operators, with particular consideration of finite rank self-commutator, the structure of invariant subspaces, and connections and applications to other fields. He will use operator theoretical tools to study the theory of quadrature domains. He also plans to investigate the structure of invariant subspaces of the Bergman space on the unit disk and multipliers between the Bergman spaces over a general bounded region. Operator theory is a central discipline in modern mathematics that studies infinite dimensional generalization of matrices. This type of research is an attempt to classify operators satisfying additional conditions given in terms of the associated operator or the underlying space. They have rich applications in every applied science as well as pure mathematics. To mention a specific example, one of basic H-infinity control problems was developed by the classical mathematical theory of Nevanlinna-Pick interpolation. Applications of the theory include improvement in automobile suspension systems, airplane flight control, chemical process control, etc.

项目摘要（项目C）主要研究者将继续研究亚正态操作员的内部结构理论，并特别考虑有限的等级自交换器，不变子空间的结构以及与其他领域的连接和应用。他将使用操作员理论工具来研究正交领域的理论。他还计划调查伯格曼空间在设备磁盘上不变的子空间的结构，以及伯格曼空间之间的乘数在一般有限区域上的乘数。 操作者理论是现代数学中的一门中央学科，研究了矩阵的无限维度概括。这种类型的研究试图对操作员进行分类，以满足相关操作员或基础空间方面给出的其他条件。 它们在每种应用科学以及纯数学中都有丰富的应用。提到一个具体的例子，基本的H-赋值控制问题之一是由Nevanlinna-Pick插值的经典数学理论开发的。该理论的应用包括改善汽车悬架系统，飞机飞行控制，化学过程控制等。