IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/713479.html
   My bibliography  Save this article

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

Author

Listed:
  • Fred Brackx
  • Nele De Schepper
  • Frank Sommen

Abstract

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called Clifford-Heaviside functions. Consequently, appropriate orthogonal polynomials on the real axis give rise to Clifford algebra-valued orthogonal polynomials in the unit ball. Three specific examples of such orthogonal polynomials in the unit ball are discussed, namely, the generalized Clifford-Jacobi polynomials, the generalized Clifford-Gegenbauer polynomials, and the shifted Clifford-Jacobi polynomials.

Suggested Citation

  • Fred Brackx & Nele De Schepper & Frank Sommen, 2004. "Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:713479
    DOI: 10.1155/S0161171204401045
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/2004/713479.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/2004/713479.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S0161171204401045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:hin:jijmms:713479. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.