Microdifferential Systems in the Complex Domain
The words "microdifferential systems in the complex domain" refer to seve ral branches of mathematics: micro local analysis, linear partial differential equations, algebra, and complex analysis. The microlocal point of view first appeared in the study of
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Editors
M. Artin S.S. Chern 1.M. Frohlich E. Heinz H. Hironaka F. Hirzebruch L. Hormander S. Mac Lane W. Magnus C.c. Moore 1.K. Moser M. Nagata W. Schmidt D.S. Scott Ya.G. Sinai 1. Tits B.L. van der Waerden M. Waldschmidt S. Watanabe Managing Editors M. Berger B. Eckmann
S.R.S. Varadhan
Pierre Schapira
Microdifferential Systems in the Complex Domain
Springer-Verlag Berlin Heidelberg N ewYork Tokyo 1985
Pierre Schapira Universite Paris Nord Departement de Mathematiques Av. 1.-B. Clement 93430 Villetaneuse France
AMS Subject Classification (1980): 58 G 05, 58 G 15, 58 G 17
Library of Congress Cataloging in Publication Data Schapira, Pierre, 1943Microdifferential systems in the complex domain. (Grundlehren der mathematischen Wissenschaften; 269) Bibliography: p. Includes index. 1. Differential equations, Partial. 2. Differential operators. 3. Cauchy problem. I. Title. II. Series. QA377.S35 1985 515.3'53 84·13981 ISBN-13: 978-3-642-64904-2 DOl: 10.1007/978-3-642-61665-5
e-ISBN-13: 978-3-642-61665-5
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "Verwertungsgesellschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1985 Softcover reprint of the hardcover 15t edition 1985
Typesetting and printing: Zechnersche Buchdruckerei, Speyer Bookbinding: J. Schaffer OHG, Griinstadt 2141/3140-543210
Preface
The words "microdifferential systems in the complex domain" refer to several branches of mathematics: micro local analysis, linear partial differential equations, algebra, and complex analysis. The microlocal point of view first appeared in the study of propagation of singularities of differential equations, and is spreading now to other fields of mathematics such as algebraic geometry or algebraic topology. However it seems that many analysts neglect very elementary tools of algebra, which forces them to confine themselves to the study of a single equation or particular square matrices, or to carryon heavy and non-intrinsic formulations when studying more general systems. On the other hand, many algebraists ignore everything about partial differential equations, such as for example the "Cauchy problem", although it is a very natural and geometrical setting of "inverse image". Our aim will be to present to the analyst the algebraic methods which naturally appear in such problems, and to make available to the algebraist some topics from the theory of partial differential equations stressing its geometrical aspects. Keeping this goal in mind, one can only remain at an elementary level. Actually the algebra we use is rather naive, and there are no fine results on partial differential equations. In that sense, the only theorem we prove here is the (micro differential) Cauchy
