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.
