Multidimensional Integral Representations Problems of Analytic Conti
The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The application
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ltidimensional Integral Representations Problems of Analytic Continuation
Multidimensional Integral Representations
Alexander M. Kytmanov • Simona G. Myslivets
Multidimensional Integral Representations Problems of Analytic Continuation
123
Alexander M. Kytmanov Institute of Mathematics and Computer Science Siberian Federal University Krasnoyarsk, Russia
Simona G. Myslivets Institute of Mathematics and Computer Science Siberian Federal University Krasnoyarsk, Russia
Multidimensional Integral Representations ISBN 978-3-319-21658-4 ISBN 978-3-319-21659-1 DOI 10.1007/978-3-319-21659-1
(eBook)
Library of Congress Control Number: 2015949242 Mathematics Subject Classification (2010): 32A25, 32A26, 32A40, 32A50 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Foreword
This monograph is devoted to integral representations for holomorphic functions in several complex variables such as: Bochner–Martinelli, Cauchy–Fantappiè, Koppelman, etc. and their applications to analytic continuation functions with a one-dimensional property of holomorphic extension. This book also contains multidimensional boundary analogues of the Morera theorem. Tel-Aviv, Israel June 2015
Lev Aizenberg
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Preface
The Bochner–Martinelli integral representation for holomorphic functions of several complex variables appeared in the works of Martinelli (1938) and Bochner (1943). It was the first essentially multidimensional representation with integration taking place over the whole boundary of the domain. This integral representation has a universal kernel (not depending on the form of the domain), like the Cauchy kernel in C1 . However, in Cn when n > 1, the Bochner–Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance hindered t
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