On the Application of Poincare-Steklov Operators to the Problem of Resonant Scattering in a Cylinder

The resonant nature of scattering in a waveguide with two barriers is proven in the case of a sufficiently arbitrary deformation of the region between the barriers. The problem is considered as an interior boundary value problem with boundary conditions defined by a Poincare-Steklov operator. A spectral problem is considered whose eigenvalue determines the resonant scattering frequency.