Complex Analysis II

The past several years have witnessed a striking number of important developments in complex analysis of both one and several variables. Through these advances the essential unity of these two previously rather separate branches of function theory has become increasingly apparent. More and more, ideas and constructs that first arose in function theory of one variable are playing an important role in the several variables theory. At the same time, techniques developed originally for use in several variables have found fruitful applications to problems in classical function theory. Examples of the former phenomenon include the development of a capacity theory for the Monge-Ampere operator and recent extensions of the Henkin-Ramirez representation formulas and their application to interpolation problems in Cn. In the second category, the systematic use of the inhomogeneous Cauchy-Riemann equation has led to important developments in the theory of H20, as well as other Banach algebras on the unit disk. It has also inspired the consideration of many new questions about open Riemann surfaces. Finally the brilliant solution of the Bieberbach Conjecture by Louis de Branges offers irrefutable testimony (as if any were needed) to the continued vitality of classical ideas and approaches.