Sturm-Liouville Theory

Past and Present

Editors: Amrein, Werner O., Hinz, Andreas M., Pearson, David B. (Eds.)

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About this book

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-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey is made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research.
The text is particularly strong on the spectral theory of Sturm-Liouville equations, which has given rise to a major branch of modern analysis. Among other current aspects of the theory discussed are oscillation theory for differential equations and Jacobi matrices, approximation of singular boundary value problems by regular ones, applications to systems of differential equations, extension of the theory to partial differential equations and to non-linear problems, and various generalizations of Borg's inverse theory. A unique feature of the book is a comprehensive catalogue of Sturm-Liouville differential equations covering more than fifty examples, together with their spectral properties. Many of these examples are connected with special functions and with problems in mathematical physics and applied mathematics.
The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Table of contents (5 chapters)

  • Sturm’s 1836 Oscillation Results Evolution of the Theory

    Don Hinton

    Pages 1-27

  • Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950

    W. Norrie Everitt

    Pages 45-74

  • Spectral Theory of Sturm-Liouville Operators Approximation by Regular Problems

    Joachim Weidmann

    Pages 75-98

  • The Titchmarsh-Weyl Eigenfunction Expansion Theorem for Sturm-Liouville Differential Equations

    Christer Bennewitz, W. Norrie Everitt

    Pages 137-171

  • Sturm’s Theorems on Zero Sets in Nonlinear Parabolic Equations

    Victor A. Galaktionov, Petra J. Harwin

    Pages 173-199

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-7643-7359-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-7643-7066-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Sturm-Liouville Theory
Book Subtitle
Past and Present
Editors
  • Werner O. Amrein
  • Andreas M. Hinz
  • David B. Pearson
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7359-7
DOI
10.1007/3-7643-7359-8
Hardcover ISBN
978-3-7643-7066-4
Edition Number
1
Number of Pages
XX, 336
Topics