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A general class of integral transforms and an expression for their convolution formulas

Journal Article


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.

Publication Date


  • 2022

Citation


  • Futcher, T., & Rodrigo, M. R. (2022). A general class of integral transforms and an expression for their convolution formulas. Integral Transforms and Special Functions, 33(2), 91-107. doi:10.1080/10652469.2021.1910255

Scopus Eid


  • 2-s2.0-85103660402

Web Of Science Accession Number


Start Page


  • 91

End Page


  • 107

Volume


  • 33

Issue


  • 2

Place Of Publication


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.

Publication Date


  • 2022

Citation


  • Futcher, T., & Rodrigo, M. R. (2022). A general class of integral transforms and an expression for their convolution formulas. Integral Transforms and Special Functions, 33(2), 91-107. doi:10.1080/10652469.2021.1910255

Scopus Eid


  • 2-s2.0-85103660402

Web Of Science Accession Number


Start Page


  • 91

End Page


  • 107

Volume


  • 33

Issue


  • 2

Place Of Publication