Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula

• Main Author: Castro, Luís Pinheiro
• Publication Date: 2019
• Other Authors: Guerra, Rita Correia, Tuan, Nguyen Minh
• Format: Article
• Language: eng
• Source: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Download full: http://hdl.handle.net/10773/26921
• topic: Convolution; Integral equation; Factorization; Fourier integral operator; Wiener-Hopf operator; Hankel operator

This paper considers two nite 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, de ned on nite 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.