On Generalized Solutions of Problems of Electromagnetic Wave Diffraction by Screens in the Closed Cylindrical Waveguides

Abstract

In this article we propose to use special classes of the generalized functions in order to state the correct statement of some diffraction problems of electromagnetic waves by thin conducting screens in the cylindrical waveguides with conducting walls. As the generalized solutions, such mappings are considered which assign a linear functional defined on the linear shell of the set of the functions satisfying the corresponding boundary conditions to every value of longitudinal space coordinate. The traces of the solutions on the cross-section of the cylindrical domain are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived immediately from the generalized boundary conditions. We show that it is advisable to use the boundary conditions for the normal components of the electromagnetic field.