On the solutions of the Moisil-Theodoresco system

A structure theorem is proved for the solutions to the Moisil-Théodoresco system in open subsets of R3. Furthermore, it is shown that the Cauchy transform maps L2(R2, R0, 2+) isomorphically onto H2(R+3, R0, 3+), thus proving an elegant generalization to R2 of the classical notion of an analytic signal on the real line.