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Volume 13
Issue 3
10.3390/math13030432
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On the Inversion of the Mellin Convolution

by
Gabriel Bengochea
1,
Manuel Ortigueira
2,* and
Fernando Arroyo-Cabañas
1
1
Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Ciudad de México 09790, Mexico
2
CTS-UNINOVA and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(3), 432; https://doi.org/10.3390/math13030432
Submission received: 24 December 2024 / Revised: 23 January 2025 / Accepted: 25 January 2025 / Published: 28 January 2025
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
Versions Notes

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.
Keywords: Sonin condition; fractional scale derivative; Mellin convolution Sonin condition; fractional scale derivative; Mellin convolution

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MDPI and ACS Style

Bengochea, G.; Ortigueira, M.; Arroyo-Cabañas, F. On the Inversion of the Mellin Convolution. Mathematics 2025, 13, 432. https://doi.org/10.3390/math13030432

AMA Style

Bengochea G, Ortigueira M, Arroyo-Cabañas F. On the Inversion of the Mellin Convolution. Mathematics. 2025; 13(3):432. https://doi.org/10.3390/math13030432

Chicago/Turabian Style

Bengochea, Gabriel, Manuel Ortigueira, and Fernando Arroyo-Cabañas. 2025. "On the Inversion of the Mellin Convolution" Mathematics 13, no. 3: 432. https://doi.org/10.3390/math13030432

APA Style

Bengochea, G., Ortigueira, M., & Arroyo-Cabañas, F. (2025). On the Inversion of the Mellin Convolution. Mathematics, 13(3), 432. https://doi.org/10.3390/math13030432

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