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Mathematics 2019, 7(3), 254; https://doi.org/10.3390/math7030254

Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Department of Mathematics, Physics, and Chemistry, Beuth University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany
Received: 18 January 2019 / Revised: 26 February 2019 / Accepted: 5 March 2019 / Published: 12 March 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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Abstract

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed. View Full-Text
Keywords: integral transforms; Laplace integral transform; transmutation operator; generating operator; integral equations; differential equations; operational calculus of Mikusinski type; Mellin integral transform integral transforms; Laplace integral transform; transmutation operator; generating operator; integral equations; differential equations; operational calculus of Mikusinski type; Mellin integral transform
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Luchko, Y. Some Schemata for Applications of the Integral Transforms of Mathematical Physics. Mathematics 2019, 7, 254.

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