Harmonic Analysis Methods and Operator Decomposability in Modern Analysis

项目摘要：该项目将关注统一抽象算符理论的发展，旨在扩大谐波分析在现代分析结构中的作用。谐波分析将用于提供频谱分解算子（和相关的削弱形式的正交性）在各种各样的背景下。将谐波分析的结构可分解性特征与算子理论相结合的机制将是A.P. Calder和Coifman-Weiss提出的迁移理论。将涉及旨在扩大迁移理论的范围和前景的研究，以及迁移理论在谐波分析中的应用。该项目的中心主题将是一个统一的概述，为将经典分析应用于其自身设置和一般数学分析提供新的途径。这些方法的广泛范围将针对适用于各种主流数学学科的新前景和发现。从人力资源的角度来看，美国国家科学基金会支持沃巴什现代分析研讨会的运作，作为中西部地区的研讨会，吸引了国内和国际的参与，将为许多年轻的研究人员和研究生提供进入知识前沿的便利，同时促进广泛的研究项目。

FOR DMS-9705475 ABSTRACT OF PROJECT BERKSON The project will be concerned with the development of a unified abstract operator theory aimed at expanding the role of harmonic analysis in the structures of modern analysis. Harmonic analysis will be used to provide spectral decomposability of operators (and associated weakened forms of orthogonality) in a wide variety of contexts. The mechanism for combining the structural decomposability features of harmonic analysis and operator theory will be the transference theory initiated by A.P. Calder n and Coifman-Weiss. Studies aimed at expanding the scope and vistas of transference theory will be involved, as will applications of transference theory to harmonic analysis. The central theme of the project will be a unified overview providing new avenues for applying classical analysis to its own settings and to general mathematical analysis. The broad scope of the methods will be aimed at new vistas and discoveries applicable to a wide variety of mainstream mathematical subjects. From the standpoint of human resources, the NSF support awarded for the operations of the Wabash Modern Analysis Seminar, which functions as a Mid-Western regional seminar attracting national and international participation, will provide ready access to the frontiers of knowledge for many young researchers and graduate students, while furthering a wide array of research programs.