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In the paper, the method of antenna synthesis, which was 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, error sensitivity coefficient, purely radiating distributions, etc.The adjoint operator transforms a desired radiation pattern into the distribution that has a number of useful properties. It can be used in various iterative algorithms for solution optimization. Moreover, it 'suggests' the rational placing of antenna elements.Quite often, there is a 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.

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This communication studies the phase pattern of an antenna, with its phase front being significantly different from a sphere. Therefore, the concept of local phase center (LPC) has been used. Two algorithms of LPC hodograph computation are presented and verified by comparison with analytical results. Even in the simplest case of two sources, a curve of the LPC hodograph may be curious and hardly predictable. This is particularly true if a special phase pattern arises, e.g., as a result of the desired amplitude pattern synthesis. Two examples with sector and secant patterns are studied and the relevant LPC-hodographs are demonstrated. All calculations prove that the LPC is unexpectedly well defined.

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