IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p432-d1578730.html
   My bibliography  Save this article

On the Inversion of the Mellin Convolution

Author

Listed:
  • Gabriel Bengochea

    (Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Ciudad de México 09790, Mexico)

  • Manuel Ortigueira

    (CTS-UNINOVA and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal)

  • Fernando Arroyo-Cabañas

    (Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Ciudad de México 09790, Mexico)

Abstract

The deconvolution of the Mellin convolution is studied for a great variety of functions that are expressed in terms of α –log-exponential monomials. It is shown that the generation of pairs of functions satisfying a Sonin-like condition can be worked as a deconvolution process. Applications of deconvolution to scale-invariant linear systems are presented.

Suggested Citation

  • Gabriel Bengochea & Manuel Ortigueira & Fernando Arroyo-Cabañas, 2025. "On the Inversion of the Mellin Convolution," Mathematics, MDPI, vol. 13(3), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:432-:d:1578730
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/432/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/432/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuri Luchko & Masahiro Yamamoto, 2020. "The General Fractional Derivative and Related Fractional Differential Equations," Mathematics, MDPI, vol. 8(12), pages 1-20, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammed Al-Refai & Yuri Luchko, 2023. "The General Fractional Integrals and Derivatives on a Finite Interval," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    3. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Vasily E. Tarasov, 2023. "General Fractional Noether Theorem and Non-Holonomic Action Principle," Mathematics, MDPI, vol. 11(20), pages 1-35, October.
    5. Maryam Al-Kandari & Latif A-M. Hanna & Yuri Luchko, 2022. "Operational Calculus for the General Fractional Derivatives of Arbitrary Order," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    6. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    7. Vasily E. Tarasov, 2023. "Multi-Kernel General Fractional Calculus of Arbitrary Order," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    8. Yuri Luchko, 2024. "On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions," Mathematics, MDPI, vol. 12(24), pages 1-18, December.
    9. Irina Petreska & Pece Trajanovski & Trifce Sandev & Jonathan A. M. Almeida Rocha & Antonio Sérgio Magalhães de Castro & Ervin K. Lenzi, 2025. "Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints," Mathematics, MDPI, vol. 13(1), pages 1-13, January.

    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:3:p:432-:d:1578730. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.