Mathematical Sciences: Operator Theory and Harmonic Analysis

数学科学：算子理论和调和分析

• 批准号: 9101959
• 负责人: Earl Berkson
• 金额: $ 9.98万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101959&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Theory; Harmonic

Professor Berkson will apply abstract operator theory and harmonic analysis to a broad range of topics in modern analysis. In recent years Professor Berkson's efforts have been directed at developing an abstract Banach space operator theory which incorporates and expands the transference methods of Coifman and Weiss. These efforts have now reached fruition, providing a unified and simplifying overview of the role of harmonic analysis in many aspects of general analysis. The present program will apply this overview to applications of central themes in analysis. The focus will be ergodic theory and its generalizations, as well as on classical and abstract harmonic analysis. The consequences for spectral theory and harmonic analysis in special spaces will be investigated. Professor Berkson's work has been in abstract operator theory. (Harmonic analysis can be considered a study of special classes of operators.) In the present project he will turn his attention to more applied topics to see how successfully the abstract ideas can be used in areas such as ergodic theory, classical analysis, and spectral theory.

Berkson教授将应用抽象算子理论， 谐波分析在现代分析中的广泛主题。 近年来，Berkson教授的努力一直针对 发展了一个抽象的Banach空间算子理论， 结合并扩展了Coifman的转移方法， 韦斯。 这些努力现已取得成果， 统一和简化谐波分析的作用概述 在一般分析的许多方面。 本方案将 将此概述应用于分析中中心主题的应用。 重点将是遍历理论及其推广，以及 经典的和抽象的谐波分析。 后果 在特殊空间中的谱理论和调和分析将是 研究了 Berkson教授的工作一直是在抽象算子理论。 （谐波分析可以被认为是对特殊类别的谐波的研究。 operators.） 在本项目中，他将把注意力转向 更多的应用主题，看看如何成功的抽象概念， 可以用于遍历理论、经典分析等领域， 光谱理论