On the structure of the solutions of the antenna synthesis problems according to the prescribed amplitude directivity pattern using the regularization functionals

It is known, that antenna synthesis problems according to the prescribed amplitude directivity pattern belong to the class of essentially incorrect problems. The absence of demands on the phase directivity pattern under the conditions of the problem should be used as an additional possibility to improve the approximation of the synthesized directivity pattern (DP) to the given one. At the same time, the the nonlinearity of the problem leads to the non-uniqueness of the solutions that complicates the process of numerically searching the solutions. In this report investigations of the quantity and quality characteristics of the existing solutions, based on the methods of functional analysis, are given in the cases of a linear antenna and antennas with plane aperture and their discrete analogy (antenna grids). It turns out that the quantity and the quality of the solutions depend on the value of the electrical size of the aperture, on the value of the space angle (where the DP is given), and on the quality of DP