IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-211-49905-4_6.html
   My bibliography  Save this book chapter

The Sousa Pinto approach to nonstandard generalised functions

In: The Strength of Nonstandard Analysis

Author

Listed:
  • R. F. Hoskins

    (Loughborough University, Department of Electronic and Electrical Engineering)

Abstract

Nonstandard Analysis suggests several ways in which the standard theories of distributions and other generalised functions could be reformulated. This paper reviews the contributions of José Sousa Pinto to this area up to his untimely death four years ago. Following the original presentation of nonstandard models for the Sebastião e Silva axiomatic treatment of distributions and ultradistributions he worked on a nonstandard theory of Sato hyperfunctions, using a simple ultrapower model of the hyperreals. (This in particular allows nonstandard representations for generalised distributions, such as those of Roumieu, Beurling, and so on.) He also considered a nonstandard theory for the generalised functions of Colombeau, and finally turned his attention to the hyperfinite representation of generalised functions, following the work of Kinoshita.

Suggested Citation

  • R. F. Hoskins, 2007. "The Sousa Pinto approach to nonstandard generalised functions," Springer Books, in: Imme van den Berg & Vítor Neves (ed.), The Strength of Nonstandard Analysis, chapter 6, pages 76-91, Springer.
    • Handle: RePEc:spr:sprchp:978-3-211-49905-4_6
    DOI: 10.1007/978-3-211-49905-4_6
    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

    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:978-3-211-49905-4_6. 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.