Biquaternionic Treatment of Inhomogeneous Time-Harmonic Maxwell's Equations Over Unbounded Domains

We study the inhomogeneous equation curl w(->) +lambda w(->) = g(->),lambda is an element of C,lambda (sic) 0 over unbounded domains in R-3, with g(->) being an integrable function whose divergence is also integrable. Most of the results rely heavily on the "good enough" behavior near infinity of the lambda Teodorescu transform, which is a classical integral operator of Clifford analysis. Some applications to inhomogeneous time-harmonic Maxwell equations are developed. Moreover, we provide necessary and sufficient conditions to guarantee that the electromagnetic fields constructed in this work satisfy the usual Silver-Muller radiation conditions. We conclude our work by showing that a particular case of our general solution of the inhomogeneous time-harmonic Maxwell equations coincide with the integral representation generated by the dyadic Green's function.