Lectures in modern analysis and applications II
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140 J. Glimm, L. Gross, Harish-Chandra, R. V. Kadison, D. Ruelle, I. E. Segal
Lectures in Modern Analysis and Applications II Edited by C. T. Taam, George Washington University
Springer-Verlag Berlin· Heidelberg· NewYork 1970
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under §.54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin' Heidelberg 1970 Library of Congress Catalog Card Number 76-94096 Printed in Germany. Title No. 3296
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 196769 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 contemporary 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 six lectures from the fifth, sixth and eighth sessions. Some of the manuscripts were proofread by the editor after they were retyped for reproduction, the editor would be grateful to have the authors' understanding in this matter which was due to the pressures of time.
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 I
Steven H. Schot American University C. T. Taam, Chairman George Washington University Elmer West Consortium of Universities
TABLE OF CONTENTS
ANALYSIS AND REPRESENTATION THEORY Professor HARISH-CHANDRA, Institute for Advanced Study Some Applications of the Schwartz Space of a Semisimple Lie Group ••••• l Let G be a semi
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