文档介绍：Applied
Functional Analysis
and
Partial Differential
Equations
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Applied
Functional Analysis
and
Partial Differential
Equations
Milan Miklavcic
Michigan State University
Vfe World Scientific
wb Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Farrer Road, Singapore 912805
USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
First published 1998
Reprinted 2001
APPLIED FUNCTIONAL ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS
Copyright © 1998 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-02-3535-6
Printed in Singapore by Uto-Print
Contents
Preface
1 Linear Operators in Banach Spaces 1
Metric Spaces 1
Vector Spaces 6
Banach Spaces 8
Linear Operators 11
Duals 16
Spectrum 23
Linear Operators 29
Boundary Value Problems for Linear ODEs 39
Exercises 43
2 Linear Operators in Hilbert Spaces 47
Orthonormal Sets 47
Adjoints 54
Accretive Operators 58
Weak Solutions 62
Example: Constant Coefficient PDEs 68
Self-adjoint Operators 70
Example: Sturm-Liouville Problem 76
Sectoria