On the polyconvolution operator with a trigonometric weight function for the Hartley integral transforms and applications

The main aim of this work is to establish a new polyconvolution operator with the weight function for the Hartley integral transforms. After that, we will apply it to solve some classes of integral equations and a system of integral equations of polyconvolution type. On the other hand, we study the Wastson-type integral transform for this polyconvolution. We establish necessary and sufficient conditions for these operators to be unitary in the space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulate the Placherel-type theorem for the aforementioned operators, prove a sequence of functions that converges to the original function in the norm of , and further show the boundedness of these operators.