Far-field patterns of solutions of the perturbed Dirac equation

摘要

The purpose of the paper is to study the asymptotic behavior at infinity of solutions of a perturbed Dirac equation in Rm called k-monogenic. Every such solution is a solution of the Helmholtz equation with values in a complex Clifford algebra. The main goal is to use the far-field pattern to characterize the radiating (outgoing) k-monogenic functions among the radiating solutions of the Helmholtz equation. It will be shown that an algebraic condition characterizes these far-field patterns.