IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i15p2435-d1712061.html
   My bibliography  Save this article

Horváth Spaces and a Representations of the Fourier Transform and Convolution

Author

Listed:
  • Emilio R. Negrín

    (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Spain
    Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Spain)

  • Benito J. González

    (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Spain
    Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Spain)

  • Jeetendrasingh Maan

    (Department of Mathematics and Scientific Computing, National Institute of Technology, Hamirpur 177005, India)

Abstract

This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces S k ′ , for k < − n . We prove that any element in S k ′ can be expressed as a finite sum of derivatives of continuous L 1 ( R n ) -functions acting on Schwartz test functions. This representation leads to an explicit expression for their distributional Fourier transform in terms of classical Fourier transforms. Additionally, we present a distributional representation for the convolution of two such elements, showing that the convolution is well-defined over S . These results deepen our understanding of non-tempered distributions and extend Fourier methods to a broader functional framework.

Suggested Citation

  • Emilio R. Negrín & Benito J. González & Jeetendrasingh Maan, 2025. "Horváth Spaces and a Representations of the Fourier Transform and Convolution," Mathematics, MDPI, vol. 13(15), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2435-:d:1712061
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/15/2435/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/15/2435/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:15:p:2435-:d:1712061. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.