IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-0667-1_36.html
   My bibliography  Save this book chapter

Indefinite Hamiltonians

In: Operator Theory

Author

Listed:
  • Michael Kaltenbäck

    (TU Wien, Institut für Analysis und Scientific Computing)

Abstract

It is the aim of the present survey to provide an introduction into the theory of indefinite Hamiltonians and to give an overview over the most important results. Indefinite Hamiltonians can be seen as a distributional generalization of the classical theory of canonical Hamiltonian differential equations as studied among many others by M.G. Kreĭn and Louis de Branges. The spaces in the background of this theory are no longer Hilbert spaces as in the classical situation, but Pontryagin spaces. This type of spaces can be seen as a Hilbert where the Hilbert space scalar product is replaced by a finite dimensional perturbation. In a similar sense indefinite Hamiltonians can be seen as a certain perturbation of classical Hamiltonians. The theory of indefinite Hamiltonians involves certain reproducing kernel Pontryagin spaces consisting of entire function which constitutes a generalization of the theory of Louis de Branges on Hilbert spaces of entire functions.

Suggested Citation

  • Michael Kaltenbäck, 2015. "Indefinite Hamiltonians," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 16, pages 373-394, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_36
    DOI: 10.1007/978-3-0348-0667-1_36
    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:978-3-0348-0667-1_36. 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.