A general class of integral transforms and an expression for their convolution formulas. Issue 2 (1st February 2022)

• Record Type: Journal Article
• Authors: Futcher, Thomas; Rodrigo, Marianito R.
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 2(2022)
• Page Start: 91
• Page End: 107
• Publication Date: 2022-02-01
• Subjects: Integral transforms -- differential equations -- convolution -- shifting property -- inversion formula; 35A22 -- 44A35 -- 34A12; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2021.1910255
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : A class of integral transforms which satisfies certain assumptions is considered. Several examples, including the Fourier, Laplace and Mellin transforms, are in this class as well as transforms which are yet to be named. The assumptions allow for certain properties to exist for these integral transforms, such as the shifting and convolution properties. Further conditions are presented which allow for the integral transform operator to be injective on a specific class of functions. Applications of the results are provided and analytical solutions to differential equations are obtained. Numerical solutions are then compared to the analytical solutions to demonstrate the usefulness of this class of transforms for solving a particular family of differential equations.