Complex Analysis I Proceedings of the Special Year held at the Unive
The past several years have witnessed a striking number of important developments in Complex Analysis. One of the characteristics of these developments has been to bridge the gap existing between the theory of functions of one and of several complex varia
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1275 Carlos A. lBerenstein (Ed.)
Complex Analysis I 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): 30-06
ISBN 3-540-18356-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18356-6 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© 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
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 these Special
Years has been to provide a forum for the exchange of ideas between the members of the department, longterm visitors and the other participants.
(In spite of the electronic mail and other gadgets, a lot of
mathematics is still done on a face to face basis!)
This time we have
had over one hundred and fifty mathematicians from several d
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