Akhiezer's theory of paired integral equations and the problem of diffraction of waves on a circular disc

We will be dealing with the theory developed in and first applied to solution of problems on diffraction of electromagnetic waves on circular openings in flat sheets. In the present article we use N.I. Akhiezer's method to solve classical problems in the mathematical theory of diffraction of waves on circular discs; these problems lead to paired integral equations of two types