Function Theory and Operator Theory via Harmonic Analysis on the Polydisc

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

The research objective of this Proposal is to conduct a deeper study of certain function theoretic concepts for Besov--Sobolev spaces of analytic functions, in one and several complex variables. Specifically, questions related to bilinear forms on spaces of analytic functions, Corona-type problems for multiplier algebras of spaces of analytic functions, and function theory on the polydisc will be approached. The main method of approach is to apply ideas and tools from harmonic analysis to address the problems raised in this proposal with the goal of resolving important and open questions arising in the areas of function and operator theory. The research program outlined in this Proposal utilizes the PI's knowledge and techniques gained from the areas of multi-parameter harmonic analysis and complex function theory to provide an array of tools by which to approach the challenging questions raised in the proposal. The proposed research is based on recent, significant contributions made by the Proposer and focuses on key questions connected to analytic functions on the disc and polydisc. The questions studied in this proposal have important connections with the areas of complex analysis, function theory, harmonic analysis and operator theory. Solutions to the research questions posed in this Proposal will have countless applications in complex analysis, function theory, harmonic analysis, and operator theory. Not only will they open the way to additional mathematical inquiry, but they will also have significant application to real-world ideas, in particular in the areas of engineering and control theory. Postdoctoral associates and graduate students will also be engaged in this project, enhancing the scientific infrastructure of the country.