Abstract
The radiation problem in a regular waveguide with inhomogeneous filling and the scattering problem in a hollow irregular waveguide are considered. The completeness of the system of waveguide root vectors is proven. The radiation conditions are set and the solvability of the excitation problem is established. The dispersion curves of the waveguide with anisotropic filling are analyzed. The singular points of dispersion curves are considered. The excitation problem for a waveguide in a resonance regimen is investigated. The embedding theorems for the vector fields are proven. The solvability of the scattering problem in a waveguide is established.
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