Analysis II
As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course ho
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Analysis II Translated from the German by Silvio Levy and Matthew Cargo
Birkhäuser Basel · Boston · Berlin
Authors: Herbert Amann Institut für Mathematik Universität Zürich Winterthurerstr. 190 8057 Zürich Switzerland e-mail: [email protected]
Joachim Escher Institut für Angewandte Mathematik Universität Hannover Welfengarten 1 30167 Hannover Germany e-mail: [email protected]
Originally published in German under the same title by Birkhäuser Verlag, Switzerland © 1999 by Birkhäuser Verlag
2000 Mathematics Subject Classification: 26-01, 26A42, 26Bxx, 30-01
Library of Congress Control Number: 2008926303
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 3-7643-7472-3 Birkhäuser Verlag, Basel – Boston – Berlin 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. For any kind of use permission of the copyright owner must be obtained.
© 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF d Printed in Germany ISBN 978-3-7643-7472-3 987654321
e-ISBN 978-3-7643-7478-5 www.birkhauser.ch
Foreword As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may find it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many. We especially thank our friends and colleages Pavol Quittner and Gieri Simonett. They have not only meticulously reviewed the entire manuscript and assisted in weeding out errors but also, through their valuable suggestions for improvement, contributed essentially to the final version. We also extend great thanks to our staff for their careful perusal of the entire manuscript and for tracking errata and inaccuracies. Our most heartfelt thank extends again to our “typesetting perfectionist”, without whose tireless effort this book would not look nearly so nice.1 We also thank Andreas for helping resolve hardware and software problems. Finally, we extend thanks to Thomas Hintermann and to Birkh¨ auser for the good working relationship and their understanding of our desired deadlines.
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