Spectral Theory of Infinite-Area Hyperbolic Surfaces
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with
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David Borthwick
Spectral Theory of Infinite-Area Hyperbolic Surfaces Second Edition
Progress in Mathematics Volume 318
Series Editors Hyman Bass Joseph Oesterlé Yuri Tschinkel Jiang-Hua Lu
More information about this series at http://www.springer.com/series/4848
David Borthwick
Spectral Theory of Infinite-Area Hyperbolic Surfaces Second Edition
David Borthwick Department of Mathematics and Computer Science Emory University Atlanta, GA, USA
ISSN 0743-1643 Progress in Mathematics ISBN 978-3-319-33875-0 DOI 10.1007/978-3-319-33877-4
ISSN 2296-505X (electronic) ISBN 978-3-319-33877-4 (eBook)
Library of Congress Control Number: 2016939135 Mathematics Subject Classification (2010): 58J50, 35P25 © Springer International Publishing Switzerland 2007, 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com)
For Sarah, Julia, and Benjamin
Preface to the Second Edition
Producing a new edition has given me the chance to discuss some of the many interesting results that have been proven since 2007. New sections have been added to later chapters of the book describing these more recent advances in our understanding of resonance distribution and spectral asymptotics for hyperbolic surfaces. In the last few years, we have also developed new techniques for the numerical computation of resonances. A new final chapter has been added describing these methods. The numerical computations are used to explore various conjectures related to resonance distribution. While I have tried to incorporate as many new results as possible, the additions have been limited by the existing scope of the book. For example, extensions of results that were already known for hyperbolic surfaces and more general manifolds in higher dimensions have not been included. I have tried to update the notes at the end of each chapt
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