Mathematical Sciences: Operator Theory and Harmonic Analysis

伯克森教授将抽象算子理论和谐波分析应用于现代分析的广泛领域。近年来，Berkson教授致力于发展抽象的巴拿赫空间算子理论，该理论结合并扩展了Coifman和Weiss的迁移方法。这些努力现已取得成果，对谐波分析在一般分析的许多方面的作用提供了统一和简化的概述。本课程将把这一概述应用于分析中的中心主题。重点将是遍历理论及其推广，以及古典和抽象的谐波分析。在特殊空间的频谱理论和谐波分析的结果将被研究。伯克森教授的工作一直是在抽象算子理论方面。（谐波分析可以被认为是对特殊类型算子的研究。）在目前的项目中，他将把注意力转向更多的应用主题，看看抽象概念如何成功地应用于遍历理论、经典分析和谱理论等领域。

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.