Introduction to Complex Theory of Differential Equations
This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thou
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Anton Savin Boris Sternin
Introduction to Complex Theory
of Differential
Equations
Frontiers in Mathematics
Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) William Y. C. Chen (Nankai University, Tianjin) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprößig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
More information about this series at http://www.springer.com/series/5388
Anton Savin • Boris Sternin
Introduction to Complex Theory of Differential Equations
Anton Savin RUDN University Department of Applied Mathematics Moscow, Russia
Boris Sternin RUDN University Department of Applied Mathematics Moscow, Russia
and
and
Leibniz Universität Hannover Institut für Analysis Hannover, Germany
Leibniz Universität Hannover Institut für Analysis Hannover, Germany
ISSN 1660-8046 ISSN 1660-8054 (electronic) Frontiers in Mathematics ISBN 978-3-319-51743-8 ISBN 978-3-319-51744-5 (eBook) DOI 10.1007/978-3-319-51744-5 Library of Congress Control Number: 2017934913 Mathematics Subject Classification (2010): 58-02, 58J32, 58Z05, 58J47, 35Gxx, 32W50, 86-XX, 78-XX © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface The present book is devoted to the complex theory of differential equations or, more precisely, to the theory of differential equations on complex-analytic manifolds. The theory of differential equations on real manifolds is very well known. At the same time, the c
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