Representations of solutions to integral equations with difference kernels on the unit disk

AbstractWe study integral equations with kernels that depend on the distance between two points. The domain of integration is the unit disk. We show how to construct the general solution to this integral equation from two specific solutions. As examples of our results, we give the solutions to the integral equations which correspond to solutions of the three-dimensional Dirichlet and Neumann problems of finding functions which are harmonic in the exterior of the unit disk