Wiener-Hopf technique for the equation U(alpha) = K(alpha) L(alpha) + D(alpha) in the case of function K(alpha) with zeroes

The solution of the Wiener-Hopf equation is provided for the problem of two dimensional wave diffraction on an impedance half-plane. The solution involves solving the Helmholz equation on a plane with mixed conditions and on an infinite plane. It is demonstrated that the solution of the Wiener-Hopf equation involves factorization and four basically distinct zero line positions.