 03309 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)
Jun 27, 03

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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 noncompact 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.
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