Next talk of the Seminar (15:10, Room Sousa Pinto):
convolutions associated with Mellin transform and
its applications in integral equations "
Anabela Silva (Department of
Mathematics & CIDMA,
University of Aveiro)
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.