Singular integral representation of the electromagnetic field as a means to correct solutions antenna problems

The article is devoted to the (singular) integral representation of the electromagnetic field ((S)IP EMF). The questions relating to the place IP EMF in electrodynamics, as well as their use for constructing a rigorous self-consistent theory of antennas, which is by far the most part is a theory of the far zone. The definition of ill-posed problem of antenna theory. Given IP EMF for the most common classes of radiating structures. The results of numerical modeling are presented.