Electrodynamics of superconducting structures: new mathematical methods and its application to the boundary value problems

This paper is focused on the development of the electrodynamic theory of superconducting structures and its application to the technique of the microwave band. The actuality of the given problem lies in the fact that nowadays there is no any acceptable mathematical methods, by means of which it would be possible to investigate in sufficient details and give designers of the radioelectronic equipment practical recommendations on solving internal and external boundary value problems (stationary and nonstationary), associated with excitation, scattering and propagation of electromagnetic waves on the superconducting (SC) objects of simple and complex shape. Therefore the developing of the electrodynamic foundations of SC structures for external and internal problems with the methods of the spectral theory is important practical task in antenna and waveguide technique.