Spectral Theory and Applications of Linear Operators and Block Operator Matrices
Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially compact operators, this volume covers both abstract and applied
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Spectral Theory and Applications of Linear Operators and Block Operator Matrices
Spectral Theory and Applications of Linear Operators and Block Operator Matrices
Aref Jeribi
Spectral Theory and Applications of Linear Operators and Block Operator Matrices
123
Aref Jeribi Department of Mathematics University of Sfax Sfax, Tunisia
ISBN 978-3-319-17565-2 ISBN 978-3-319-17566-9 (eBook) DOI 10.1007/978-3-319-17566-9 Library of Congress Control Number: 2015102923 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)
To my mother Sania, my father Ali, my wife Fadoua, my children Adam and Rahma, my brothers Sofien and Mohamed Amin, my sister Elhem, my mother-in-law Zineb, my father-in-law Ridha, and all members of my extended family
Preface
Several books have been devoted to the spectral theory and its applications. However, this volume is very special as compared with the previous ones. For example, the perturbation approach has been, for a long time, extensively studied and considered as one of the most useful methods used in order to study some mathematical and applied problems. The main idea is that, if we know something about the solution for an easier problem, lying “close” to the one we are studying, then we can say something about our problem, provided that the difference or the perturbation is sufficiently weak. In view of more advanced applications, especially the ones dealing with complicated evolutional problems in Physics, Chemistry, Technology, Biology, etc., where the natural setting doesn’t involve single operators but operator matrices and polynomial operator pencils, the concept of compact perturbations is very often used, and it was shown that they were not sufficient for handling such problems. The main advantage of th
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