Rupert L. Frank
On the spectral analysis and scattering theory of the Laplacian on the 
halfplane with a periodic perturbation on the boundary
(609K, Postscript)

ABSTRACT.  We study the spectrum of the Laplacian $H^(\sigma)=-\Delta$ on 
$L_2(\R^2_+)$ corresponding to the boundary condition 
$\frac{\partial u}{\partial \nu}+\sigma u=0$ for a wide class of 
periodic functions $\sigma$. The Floquet decomposition leads to 
problems on a non-compact cell, which are analyzed in detail. This 
allows us to prove under the condition $\sigma\geq0$ that $H^(\sigma)$ 
is unitarily equivalent to the Neumann Laplacian $H^(0)$, the 
equivalence being provided by the wave operators. In the general case 
the existence of additional channels of scattering is investigated, 
which are due to (possibly embedded) eigenvalues of the problems from 
the Floquet decomposition.