The sommerfeld half-plane problem revisited I: The solution of a pair of coupled Wiener-Hopf integral equations

A study and the solution of an extension of the classical Sommerfeld half-plane problem which leads to a pair of integral equations of the Wiener-Hopf type is given. The method of solution is function theoretic in character and employs a combination of the ideas of Wiener and Hopf and Carleman.