Two-dimensional (P,Q)-Mellin transform and applications

Abstract

In this paper, we have introduced and studied two-dimensional [Formula: see text]-Mellin transform which extends the known results of two-dimensional [Formula: see text]-Mellin transform. We provide its several basic properties, the appropriate convolution, the inversion formula and the Parseval-type relations. Some applications of [Formula: see text]-Mellin transform have been pointed out in solving integral equations. Finally, a Titchmarsh-type theorem has been proved.