Convolutions of the fourier-cosine and fourier-sine integral transforms and integral equations of the convolution type

Abstract

This paper introduces general definitions of convolutions without and with weight, obtains four new convolutions and generalized convolutions of the Fourier-cosine and Fourier-sine integral transforms. Furthermore, the paper investigates into a class of integral equations with the mixed Toeplitz-Hankel kernel. Namely, by using the constructed convolutions the explicit solutions are obtained.