Complex Analysis II Proceedings of the Special Year held at the Univ
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1276 Carlos A. Berenstein (Ed.)
Complex Analysis II Proceedings of the Special Year held at the University of Maryland, College Park, 1985-86
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann Subseries: Department of Mathematics, University of Maryland Adviser: M. Zedek
1276 Carlos A. Berenstein (Ed.)
Complex Analysis II Proceedings of the Special Year held at the University of Maryland, College Park, 1985-86
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editor
Carlos A. Berenstein Department of Mathematics, University of Maryland College Park, MD 20742, USA
Mathematics Subject Classification (1980): 32-06 ISBN 3-540-18357-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18357-4 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
INTRODUCTION 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 devel-
oped 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 MongeAmpere operator and recent extensions of the HenkinRamirez representation formulas and their application to interpolation problems in
tn.
In the second category, the systematic use of the inho-
mogeneous CauchyRiemann equation has led to important developments in the theory of Hoo, 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. It is in this context that the Department of Mathematics of the University of Maryland decided to dedicate its sixteenth Special Year to the subject of Complex Analysis.
The objective of t
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