Hankel Operators and Their Applications
This book is a systematic presentation of the theory of Hankel operators. It covers the many different areas of Hankel operators and presents a broad range of applications, such as approximation theory, prediction theory, and control theory. The author ha
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Vladimir V. Peller
Hankel Operators and Their Applications
,
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Vladimir Peller Department of Mathematics Michigan State University East Lansing, MI48824-1027 USA [email protected]
Mathematics Subject Classification (2000): 47-02, 47B35 Library of Congress Cataloging-in-Publication Data Peller, Vladimir. Hankel operators and their applications / Vladimir Peller. p. ern. - (Springer monographs in mathematics) Includes bibliographical references and indexes. ISBN 978-1-4419-3050-7 ISBN 978-0-387-21681-2 (eBook) DOl 10.1007/978-0-387-21681-2 1. Hankel operators. QA329.6.P45 2002 515'.723--dc21
I. Title.
II. Series. 2002026656
Printed on acid-free paper. © 2003 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 15t edition 2003 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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SPIN 10887022
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Preface
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic functions. Hankel operators can be defined as operators having infinite Hankel matrices (i.e., matrices with entries depending only on the sum of the coordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Hankel matrices was obtained by Kronecker, who characterized Hankel matrices of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1,
