On the polyconvolution with a weight function for Fourier cosine, Fourier and Fourier sine transforms

摘要

The polyconvolution*~γ(f,g,h)(x) of three functions f,g,h is constructed for the integral transforms Fourier cosine (F_c), Fourier (F), and the Fourier sine (F_s), whose factorization equality is of the form F_c(*γ(f,g,h))(y) = e ~(-y)(Ff)(y).(F_sg)(y).(F_sh)(y), ?y > 0. Its properties and applications in solving systems of integral equations are presented.