Functional Analysis in Mechanics
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Springer
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L.P. Lebedev
LL V orovich
Functional Analysis in Mechanics
Springer
L.P. Lebedev Departamento de Matematicas Universidad Nacional de Colombia Bogota Colombia [email protected]
1.1. V orovich (deceased)
Mathematics Subject Classification (2000): 46-01, 35-01, 74-01, 76-01, 74Kxx, 35Dxx, 35Qxx Library of Congress Cataloging-in-Publication Data Lebedev, L.P Functional analysis in mechanics / L.P. Lebedev, LI. Vorovich. p. cm. - (Springer monographs in mathematics) Includes bibliographical references and index. 1. Functional analysis. QA320 .L3483 2002 5l5'.7-dc2l
I. Lebedev, Leonid Petrovich, 1946- II. Title.
III. Series.
2002075732
Printed on acid-free paper. ISBN 978-1-4419-3035-4 DOl 10.1 007/978-0-387-22725-2
ISBN 978-0-387-22725-2 (eBook)
© 2003 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover 1st 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.
9 8 7 6 5 432 1
SPIN 10881937
Typesetting: Pages created by the authors using a Springer LaTeX 2e macro package. www.springer-ny.com Springer-Verlag New York Berlin Heidelberg A member of Berte/smannSpringer Science+Business Media GmbH
Preface to the English Edition
This book started about 30 years ago as a course of lectures on functional analysis given by a youthful Prof. 1.1. Vorovich to his students in the Department of Mathematics and Mechanics (division of Mechanics) at Rostov State University. That course was subsequently extended through the offering, to those same students, of another course called Applications of Functional Analysis. Later, the courses were given to pure mathematicians, and even to engineers, by both coauthors. Although experts in mechanics are quick to accept results concerning uniqueness or non-uniqueness of solutions, many of these same practitioners seem to hold a rather negative view concerning theorems of existence. Our goal was to overcome this attitude of reluctance toward existence theorems, and to show that functional analysis does contain general ideas that are useful in applications. This book was written on the basis of our lectures, and was then extended by the inclusion of some original results which, although not very new, are still not too well known. We mentioned that our lectures were given to students of the Division of Mechanics. It s
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