power criterion

The antenna synthesis problem according to the prescribed power radiation pattern with the equality norm condition is considered. It is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The Lagrange--Euler equation for obtained functional is a nonlinear integral equation of the Hammerstein type. The polynomial approach is described for a generalized equation of this type, which holds for different types of antennas.