Fourier Integral Operators

This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic g

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Fourier Integral Operators

J.J. Duistermaat

Reprint of the 1996 Edition

§> Birkhauser

J.J. Duistermaat (deceased)

Originally published as Volume 130 in the series Progress in Mathematics

ISBN 978-0-8176-8107-4 e-ISBN 978-0-8176-8108-1 DOI 10.1007/978-0-8176-8108-1 ISBN 978-0-8176-8107-4 e-ISBN 978-0-8176-8108-1 Springer New York Dordrecht Heidelberg London

DOI 10.1007/978-0-8176-8108-1

Library of New Congress Control Number: xxxxxxxxxx Springer York Dordrecht Heidelberg London © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper www.birkhauser-science.com

J. J. Duistermaat

Fourier Integral Operators

Birkhauser Boston • Basel • Berlin

J. J. Duistermaat Mathematics Institute Universiteit Utrecht 3508 TA Utrecht The Netherlands

Library of Congress Cataloging-in-Publication Data Duistermaat, J. J. (Johannes Jisse), 1942Fourier integral operators / J. J. Duistermaat p. cm. — (Progress in mathematics ; v. 130) Includes bibliographical references. ISBN 0-8176-3821-0 (h : acid free). --ISBN 3-7643-3821-0 (h acid free) 1. Fourier integral operators. 2. Fourier series. I. Title. II. Series: Progress in mathematics (Boston, Mass.) ; vol. 130. QA329.6.D843 1995 95-35173 515'.723-dc20 CIP

Printed on acid-free paper

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© Birkhauser Boston 1996 Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Birkhauser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be addressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. ISBN 0-8176-3821-0 ISBN 3-7643-3821-0 Layout and typesetting by Martin Stock, Cambridge, MA Printed and bound by Quinn-Woodbine, Woodbine, NJ Printed in the U.S.A. 9 8 7 6 5 4 3 2 1

Contents Preface 0. Introduction 1. Preliminaries 1.1. Distribution densi