Differential Equations with Operator Coefficients with Applications
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Springer-Verlag Berlin Heidelberg GmbH
Vladimir Kozlov • Vladimir Maz'ya
Differential Equations with Operator Coefficients with Applications to Boundary Value Problems for Partial Differential Equations
,
Springer
Vladimir Kozlov Vladimir Maz'ya Linkoping University Department of Mathematics 58183 Linkoping Sweden
LIbrary of Congress Cataloging-in-Publication Data Kozlov, V1adimir,1954Differential equations with operator coefficients with applications to boundary value problems for partial differential equations I Vladimir Kozlov, Vladimir Maz'ya. p.cm.-- (Springer monographs in mathematics) Includes bibliographical references and indexes. ISBN 978-3-642-08453-9 ISBN 978-3-662-11555-8 (eBook) DOI 10.1007/978-3-662-11555-8 I. Differential equations. 2. Differential operators. 3. Boundary value problems. 1. Maz'ia, V. G. II. Title. III. Series. QA372.K853 1999 515'.35--ddc21
Mathematics Subject Classification (1991): Primary 47-02; Secondary 34Gxx, 3SBxx, 3SB40, 47FOS
ISBN 978-3-642-08453-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-VerIag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. @ Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999 Softcover reprint of the hardcover 1st edition 1999 The use of general descriptive names, registered names, trademarks 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.
SPIN 10690912
4113143-543210 - Printed on acid-free paper
Table of Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XV
Part I. Differential Equations with Constant Operator Coefficients 1.
2.
Power-Exponential Zeros........................ ....... 1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Basics on Operator Pencils. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Decomposition of the Resolvent Near the Pole. . . . 1.2.3 Two-Term Quadratic Pencils . . . . . . . . . . . . . . . . . . . 1.3 Power-Exponential Solutions of the Homogeneous Equation 1.3.1 Notation. Spaces Z(A, All) and Z(A*, 'Xv). . . . . . . . . 1.3.2 A Biorthogonality Condition. . .. . . . . . . . . . . . . . . . 1.3.3 Proof of Proposition 1.3.1 . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Tw
