New convolutions associated with the Mellin transform and their applications in integral equations

• Author(s): Castro, L. P. ; Silva, A. S. ; Tuan, N. M.
• Date: 2020
• Persistent ID: http://hdl.handle.net/10773/31020
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Convolution; Mellin transform; Convolution operator; Factorization; Integral equations of the convolution type
• Document Type: Journal article
• Language: English

Description

In this paper, we introduce two new convolutions associated with the Mellin transform which exhibit factorization properties upon the use of certain weight functions. This is applied to the solvability analysis of classes of integral equations. In particular, we present sufficient conditions for the solvability of an integral equation and a system of integral equations of convolution type.