On a certain class of integral equations associated with Hankel transforms

This paper deals with a new class of Fredholm integral equations of the first kind associated with Hankel transforms of integer order. Analysis of the equations is based on operators transforming Bessel functions of the first kind into kernels of Weber-Orr integral transforms. Their inverse operators are established by means of new inversion theorems for the Hankel and Weber-Orr integral transforms of functions belonging to L-1 and L-2. These operators together with the proven Paley-Wiener's theorem for the Weber-Orr transform enable to regularize the equations and, in special cases, to derive explicit solutions. The integral equations analyzed in this paper can be employed instead of dual integral equations usually treated with the Cooke-Lebedev method. An example manifests that it may be preferable because of the possibility to control norms of operators in the regularized equations.