Integral representations in boundary-value problems on calculation of devices of microwave and EHF bands

In the electrodynamic calculation of microwave (EHF) devices using methods that lead to algorithms in an open form, strict integral relations (representations) are very useful: Lorentz lemma, reciprocity theorem, orthogonality condition for eigenwaves, etc. of the results obtained, their convergence improves, and in some cases the calculation of characteristics that cannot be calculated without the indicated representations. Integral representations are a record of the equations of electrodynamics (in any unified form) and their solutions in one or another generalized form, linking in general the electromagnetic fields in electrodynamic structures described by boundary value problems. Integral views are used to control the results obtained; insome cases, they allow obtaining analytical solutions; lead to self-consistent problems that take into account the reverse effect of the radiation field on the primary sources; allow obtaining a priori information about the spectrum of possible solutions; solve associated problems as specific problems of arousal. Consideration of the phenomenon of complex resonance in this work shows that integral representations make it possible to establish a connection between non-self-adjointness and self-consistency of boundary value problems.