A novel polyconvolution for the Fourier sine, Fourier cosine and the Kontorovich–Lebedev integral transforms and applications

Abstract. The polyconvolution \(\mathop{\ast }\limits_1(f,g,h)(x)\) of three functions \(f, ~g,~ h\) is constructed for the integral transforms Fourier sine \((F_s)\), Fourier cosine \((F_c)\) and Kontorovich–Lebedev \((K_{iy})\), whose factorization equality is of the form $$ F_s(\mathop{\ast }\limits_1(f, g, h))(y) = (F_sf)(y).(F_cg)(y). (K_{iy}h), \; \forall y > 0. $$ Relations of this polyconvolution to the Fourier convolution and the Fourier cosine convolution and also relations between the new polyconvolution product and other known convolution products are established. Then we give applications to solving a class of generalized integral equations with Toeplitz plus Hankel kernel.