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 γ = sin ⁡ y 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 L 2 (R) 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 L 2 (R) , and further show the boundedness of these operators. [ABSTRACT FROM AUTHOR]