Holomorphic Function Theory in Several Variables An Introduction
This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and
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Christine Laurent-Thiébaut
Holomorphic Function Theory in Several Variables An Introduction
Christine Laurent-Thiébaut Université Joseph Fourier Institut Fourier B.P. 74 38402 Saint-Martin d’Hères Cedex France [email protected] Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Universitá degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus J. Macintyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor A. Woyczynski, Case Western Reserve University EDP Sciences ISBN 978-2-7598-0364-4 Translation from the French language edition: Théorie des fonctions holomorphes de plusieurs variables by Christine Laurent-Thiébaut Copyright © 1997 EDP Sciences, CNRS Editions, France. http://www.edpsciences.org/ http://www.cnrseditions.fr/ All Rights Reserved ISBN 978-0-85729-029-8 e-ISBN 978-0-85729-030-4 DOI 10.1007/978-0-85729-030-4 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010934643 Mathematics Subject Classification (2000): 32A26, 32D05, 32D20 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, et cetera, in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: SPI Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI I
Elementary local properties of holomorphic functions of several complex variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Notation and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The Cauchy formula for polyd
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