Editorial Board David Cox Walter Craig Nikolai Ivanov Steven G. Krantz David Saltman (Chair) This work was originally published in French by E D P Science, Paris, under the title "Operateurs pseudo-different iels et theoreme de Nash-Moser" © 1991 InterEdit ions and Editions de CNRS. Th e present translation was created under license for the American Mathematical Society and is published by permission. Translated by Stephen S. Wilson 2000 Mathematics Subject Classification. Primary 35-02 Secondary 35Sxx, 47G30, 47N20. For additional information and updates on this book, visit w w w . a m s . o r g / b o o k p a g e s / g s m - 8 2 Library of Congress Cataloging-in-Publication Data Alinhac, S. (Serge) [Operateurs pseudo-differentiels et theoreme de Nash-Moser. English] Pseudo-differential operators and the Nash-Moser theorem / Serge Alinhac, Patrick Gerard translated by Stephen S. Wilson. p. cm. Includes bibliographical references and index. ISBN 978-0-8218-3454-1 (alk. paper) 1. Pseudodifferential operators. 2. Implicit functions. I. Gerard, Patrick, 1961- II. Title. QA329.7.A4513 2007 515/.7242—dc22 2006047985 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permission@ams.org. © 2007 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at h t t p : //www. ams. org/ 10 9 8 7 6 5 4 3 2 1 12 11 10 09 08 07
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