On some boundary value problems on a strip in the complex plane

The Sommerfeld integral inversion method for the Helmholtz equation in an angular region with different boundary values leads to boundary value problems in an infinite strip of the complex plane. We investigate a generic system for such boundary value problems and give the existence and uniqueness results with optimal growth estimates on the solution. We also give the solutions of the Dirichlet problem in a strip when the boundary functions grow exponentially.