Resolvent approach to the Fourier method in a mixed problem for the wave equation

The method of contour integration as applied to the resolvent of the spectral problem is used to substantiate the Fourier method in a mixed problem for the wave equation with a complex potential and boundary conditions generalizing free-end boundary conditions. Minimum smoothness assumptions are made about the initial data. Krylov’s technique of accelerating the convergence of the Fourier method is essentially employed.