Generalized translation and convolution operators in the realm of linear canonical deformed Hankel transform with applications

Hatem Mejjaoli; Firdous A. Shah; Nadia Sraieb

doi:10.56754/0719-0646.2801.105

DOI:

https://doi.org/10.56754/0719-0646.2801.105

Abstract

Among the class of generalized Fourier transformations, the linear canonical transform is of pivotal importance mainly due to its higher degrees of freedom in lieu of the conventional Fourier and fractional Fourier transforms. This article is a continuation of our recent work "Linear canonical deformed Hankel transform and the associated uncertainty principles, J. Pseudo-Differ. Oper. Appl.(2023), 14:29". Building upon this, we formulate the generalized translation and convolution operators associated with this newly proposed transformation. Besides, the obtained results are invoked to examine and obtain an analytical solution of the generalized heat equation. Finally, we study the heat semigroup pertaining to the generalized heat equation.

Keywords

Deformed Hankel transform , linear canonical deformed Hankel transform , generalized translation , generalized convolution , heat semigroup , heat equation

Mathematics Subject Classification:

47G10 , 42B10 , 47G30

Hatem Mejjaoli Taibah University, College of Sciences, Department of Mathematics, PO BOX 30002 Al Madinah AL Munawarah, Saudi Arabia. https://orcid.org/0000-0003-1979-7104
Firdous A. Shah Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India. https://orcid.org/0000-0001-8461-869X
Nadia Sraieb Department of Mathematics, Faculty Sciences of Gabes, Gabes Universit, Omar Ibn Khattab Street 6029 Gabes, Tunisia. https://orcid.org/0000-0002-7111-1918

Pages: 105–147
Date Published: 2026-01-27
Vol. 28 No. 1 (2026)

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