Inverse source reconstruction for the synthesis on conformal domains

The inverse problem of the synthesis of conformal antennas is dealt with by referring to the spectral decomposition of the relevant linear operator. The source is supposed to lay on an arc of circumference since this allows to evaluate the number of degrees of freedom of the radiated field. This result, that can be obtained in closed form for a continuous source, is useful to analyze also the discrete case. Numerical examples of the synthesis of focusing beams pointing at different directions are provided to show the role of the source geometry.