In this report, the method of antenna synthesis that has been proposed and developed by V.N. Dymsky and extended by his disciples is presented. It combines mathematical formalism of functional spaces and profound physical interpretation. Some original concepts are introduced, such as the power radiated in the desired antenna pattern, the pattern’s relief deviation, coefficient of error sensitivity, purely radiating distributions, etc.

The adjoint operator transforms a desired radiation pattern in the distribution, which has a number of useful properties. It can be used in various iterative algorithms for solution optimization. Moreover, it ‘suggests’ rational placing of antenna elements.

Quite often, there is need to synthesize the desired radiation pattern and at the same time meet rigorous requirements for the near field's structure. The way to extend the adjoint operator method to such tasks is discussed.

Numerous calculations illustrate the main results.