Functional Analysis and Applications Seminar


(organized by the Functional Analysis and Applications Group)


Department of Mathematics, University of Aveiro




Next talk of the Seminar (15:10, Room Sousa Pinto):


11/12/2019: "New convolutions associated with Mellin transform and its applications in integral equations "



Anabela Silva  (Department of  Mathematics &  CIDMA, University of Aveiro)



The main purpose of this talk is to present two new convolutions associated with the Mellin transform and in the framework of Lebesgue spaces. One of the most important properties of a convolution is to satisfy a factorization property which is typically associated with one or more than one integral operators (the Convolution Theorem). In most of the cases, such factorization property is fundamental to solve consequent integral equations which can be characterized by those convolutions. In this sense, we show that the convolutions introduced exhibit certain factorization identities when considering the integral operators under study. As applications, we present the solvability of an integral equation and a system of integral equations of new convolution type.




This Seminar is supported in part by the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2019.



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