Sturm-Liouville Theory Past and Present
This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouv
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Birkhäuser Verlag Basel Boston Berlin •
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Editors: Werner O. Amrein Section de Physique Université de Genève 24, quai Ernest-Ansermet 1211 Genève 4 Switzerland [email protected]
Andreas M. Hinz Mathematisches Institut Universität München Theresienstrasse 39 D-80333 München Germany [email protected]
David P. Pearson Department of Mathematics University of Hull Cottingham Road Hull HU6 7RX United Kingdom [email protected]
2000 Mathematical Subject Classification 34B24, 34C10, 34L05, 34L10, 01A55, 01A10
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 3-7643-7066-1 Birkhäuser Verlag, Basel – Boston – Berlin 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2005 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Cover design: Micha Lotrovsky, CH-4106 Therwil, Switzerland Printed on acid-free paper produced of chlorine-free pulp. TCF °° Printed in Germany ISBN-10: 3-7643-7066-1 ISBN-13: 978-3-7643-7066-4 987654321
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Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
Scientific Lectures given at the Sturm Colloquium . . . . . . . . . . . . . . . . . . . . . . . . .
x
Introduction (David Pearson) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
Don Hinton Sturm’s 1836 Oscillation Results. Evolution of the Theory . . . . . . . . . . .
1
Barry Simon Sturm Oscillation and Comparison Theorems . . . . . . . . . . . . . . . . . . . . . . . .
29
W. Norrie Everitt Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Joachim Weidmann Spectral Theory of Sturm-Liouville Operators. Approximation by Regular Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
Yoram Last Spectral Theory of Sturm-Liouville Operators on Infinite Intervals: A Review of Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Daphne Gilbert Asymptotic Methods in the Spectral Analysis of Sturm-Liouville Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121
Christer Bennewitz and W. Norrie Everitt The Titchmarsh-Weyl Eigenfunction Expansion Theorem for Sturm-Liouville Differential Equations
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