Scattering theory for bulk and surface waves in an impedance half-space, I: radiation conditions and a Rellich-type theorem

We study the negative Laplacian on the half-space $\mathbb{R}^n_+$, $n \ge 3$, subject to a constant impedance (Robin) boundary condition with $α> 0$. The boundary then carries a bound transverse mode, and at each energy $E > 0$ the system propagates two channels with the distinct wavenumbers $\sqrt