Far-field patterns of solutions of the perturbed Dirac equation (Q2846209)

As is the case for the Laplace operator, in Euclidean Clifford analysis also the Helmholtz operator can be factorized, more precisely by using perturbed Dirac operators. In the paper the authors study the asymptotic behaviour at infinity of special solutions of the associated Helmholtz equation with values in a complex Clifford algebra, which are, in fact, solutions of the perturbed Dirac operators involved and called \(k\)-monogenic. The main goal is to use the far-field pattern to characterize the radiating \(k\)-monogenic functions among those solutions of the Helmholtz equation. An algebraic condition characterizing these far-field patterns is given.