On the Laplace generalized convolution transform

Abstract. Several classes of integral transforms related to Laplace generalized convolution are studied. Necessary and sufficient conditions to ensure that the transformation is unitary are obtained, and a formula for the inverse transformation is derived in this case. In the application, we obtain solutions of several classes of integro-differential equations in closed form.

Key words and phrases. Convolution, Fourier sine, Fourier cosine, Laplace transform, integro-differential equation.