Representations of solutions to integral equations with difference kernels on the unit disk (Q1066409)

The author considers an integral equation of the form (1) \(\alpha u+\beta \Gamma u=f(x)\), \(x\in D\), where D denotes the unit disc in \(R^ 2\), \(\alpha\) is a constant, \(\beta\) denotes a linear differential operator with constant coefficients, and \(\Gamma\) is a two-dimensional integral operator with a kernel that depends on the distance between two points. He shows how to construct the general solution of (1) from two specific solutions, which correspond to right-hand sides expressed in terms of the Bessel functions of the first kind of order 0, and 1, respectively.