IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7643-7359-7_3.html
   My bibliography  Save this book chapter

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

In: Sturm-Liouville Theory

Author

Listed:
  • W. Norrie Everitt

    (University of Birmingham Edgbaston, School of Mathematics and Statistics)

Abstract

The first joint publication by Sturm and Liouville in 1837 introduced the general theory of Sturm-Liouville differential equations. This present paper is concerned with the remarkable development in the theory of Sturm-Liouville boundary value problems, which took place during the years from 1900 to 1950. Whilst many mathematicians contributed to Sturm-Liouville theory in this period, this manuscript is concerned with the early work of Sturm and Liouville (1837) and then the contributions of Hermann Weyl (1910), A.C. Dixon (1912), M.H. Stone (1932) and E.C. Titchmarsh (1940 to 1950). The results of Weyl and Titchmarsh are essentially derived within classical, real and complex mathematical analysis. The results of Stone apply to examples of self-adjoint operators in the abstract theory of Hilbert spaces and in the theory of ordinary linear differential equations. In addition to giving some details of these varied contributions an attempt is made to show the interaction between these two different methods of studying Sturm-Liouville theory.

Suggested Citation

  • W. Norrie Everitt, 2005. "Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950," Springer Books, in: Werner O. Amrein & Andreas M. Hinz & David P. Pearson (ed.), Sturm-Liouville Theory, pages 45-74, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7359-7_3
    DOI: 10.1007/3-7643-7359-8_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-7643-7359-7_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.