Analysis of Toeplitz Operators
Since the late 1980s, Toeplitz operators and matrices have remained a ?eld of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplit
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Albrecht Böttcher · Bernd Silbermann
Analysis of Toeplitz Operators Second Edition Prepared jointly with Alexei Karlovich
With 20 Figures
123
Albrecht Böttcher Bernd Silbermann Technische Universität Chemnitz Fakultät für Mathematik 09107 Chemnitz, Germany [email protected] [email protected]
Library of Congress Control Number: 2006922574
Mathematics Subject Classification (2000): 47-02, 15A15, 30D55, 42A50, 45E10, 46E25, 47B35, 47L15, 65F99 ISSN 1439-7382 ISBN-10 3-540-32434-8 Springer-Verlag Berlin Heidelberg New York ISBN-13 978-3-540-32434-8 Springer-Verlag Berlin Heidelberg New York ISBN 3-540-52147-X 1st ed. Springer-Verlag Berlin Heidelberg New York (co-publication) 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 © Akademie-Verlag Berlin 1990 First Edition Printed in Germany 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. Typesetting by the authors using a Springer TEX macro package Production and data conversion: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
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Preface to the Second Edition
Since the late 1980s, Toeplitz operators and matrices have remained a field of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators confirmed their role as the basic elementary building blocks of more complicated operators on the other. Several monographs on Toeplitz and Hankel operators were written during the last decade. These include Peller’s grandiose book on Hankel operators and their applications and Nikolski’s beautiful easy reading on operators, functions, and systems, with emphasis on topics connected with the names of Hardy, Hankel, and Toeplitz. They also include books by the authors together with Hagen, Roch, Yu. Karlovich, Spitkovsky, Grudsky, and Rabinovich. Thus, results, techniques, and developments in the field of Toeplitz operators are now well presented in the monographic literature. Despite these competitive works, we felt that large parts of the first edition of the present monogra
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