Lectures in Modern Analysis and Applications I
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103 M. F. Atiyah, J. Eells, K. M. Hoffman, L. Hormander, C. E. Rickart, H. Rossi, S. Smale, F. Treves, J. Wermer
Lectures in Modern Analysis and Applications I Edited by C. T. Taam, George Washington University
Springer-Verlag Berlin · Heidelberg · New York 1969
All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer Verlag. © by Springer- Verlag Berlin · Heidelberg 1969 Library of Congress Catalog Card Number 76-94096. Printed in Germany. Title No. 3709
PREFACE This lecture series in Modern Analysis and Applications was sponsored by the Consortium of Universities ( American University, Catholic University, Georgetown University, George Washington University, and Howard University ) in Washington, D. C. and the University of Maryland, in conjunction with the U. S. Air Force Office of Scientific Research. These lectures were presented at the sponsoring universities over the period 1967-69 by mathematicians who have contributed much to the recent growth of analysis. The series consisted of eight (8) sessions of three lectures each. Each session was devoted to an active basic area of contem-----porary analysis which is important in application or shows potential applications. Each lecture presented a survey and a critical review of certain aspects of that area, with emphasis on ~ result,, open problem, and application. The eight sessions of the series were devoted to the following basic areas of analysis: 1. 2. 3. 4. 5. 6. 7. 8.
Modern Methods and New Results in Complex Analysis Banach Algebras and Applications Topological Linear Spaces and Applications Geometric and Qualitative Aspects of Analysis Analysis and Representation Theory Modern Analysis and New Physical Theories Modern Harmonic Analysis and Applications Integration in Function Spaces and Applications.
This volume contains nine lectures from the first four sessions. Other lectures will appear in subsequent volumes.
C. T. Taam George Washington University
ORGANIZING COMMITTEE
George H. Butcher Howard University Avron Douglis University of Maryland John E. Lagnese Georgetown University Raymond W. Moller Catholic University of America Robert G. Pohrer U. S. Air Force Office of Scientific Research Steven H. Schot American University C. T. Taam, Chairman George Washington University Elmer West Consortium of Universities
TABLE OF CONTENTS
MODERN METHODS AND NEW RESULTS IN COMPLEX ANALYSIS Professor KENNETH M. HOFFMAN, Massachusetts Institute of Technology Bounded Analytic Functions in the Unit Disk ••••••••••••••••••••.•• 1 A discussion of the compactification of the unit disc which is induced by the algebra of bounded analytic functions, especially Carleson's work on the corona theorem and the speaker's work on analytic subsets of the compactification. Professor HUGO ROSSI, Brandeis University Strongly Pseudoconvex Domains • . • • • • • • • . • . • • • • • • • • • • • • • • . • • • • • • • • • 10 Some of the most exciting work in several complex variables done in the past ten y
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