On the polyconvolution operator related to Hartley integral transforms H1,H2,H2 and its applications

Abstract

This research is focused to introduce the new polyconvolution operator related to Hartley integral transforms [Formula: see text] study the algebraic fundamental properties, and at the same time, we apply this polyconvolution operator to solve an integral equation of polyconvolutions type, integro-differential equation of Barbashin type and a system of two integral equations of polyconvolution type. On the other hand, we study the Wastson-type integral for this polyconvolution operator. We establish necessary and sufficient conditions for these operators to be unitary in the space [Formula: see text] and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulate the Placherel-type theorem for the aforementioned operators, proved a sequence of function that convergence to the original function in the norm of [Formula: see text] and further show the boundedness of these operators.