The Solution of the Boundary Problem for an Arbitrary Elliptic Operator Satisfying the Radiation Condition

Abstract

The scalar problem of oscillation excitation in the cylindrical waveguide, when the contraction of the operator on the cross section perpendicular to waveguide's axis is an arbitrary elliptic operator, and the boundary condition is the condition of the third kind is considered. It's shown, that it's effective to use the method of generalized Fourier-transformation for such a problem, and the requirement of generalized Fourier-transform existence is the condition, singling the solution, that is the superposition of waves propagating from the source