Abstract
This paper considers two finite integral transforms of Fourier-type, in view to propose a set of eight new convolutions, and to analyze the solvability of a class of the integral equations of Wiener-Hopf plus Hankel type, defined on finite intervals, which is involved in engineering problems. The solvability and solution of the considered equations are investigated by means of Fourier-type series, and a Shannon-type sampling formula is obtained. Some concluding remarks with respect to theoretical issues and engineering applications are emphasized in the last section, along with the analysis of some illustrative cases, which exemplify that the present method solves cases which are not under the conditions of previously known techniques.
This work was supported in part by FCT-Portuguese Foundation for Science and Technology through the Center for Research and Development in Mathematics and Applications (CIDMA) of Universidade de Aveiro, within project UID/MAT/04106/2019, and by the Viet Nam National Foundation for Science and Technology Development (NAFOSTED). R. C. Guerra also acknowledges the direct support of the Portuguese Foundation for Science and Technology (FCT) through the scholarship PD/BD/114187/2016.
(Communicated by Gregor Dolinar)
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