 04407 Rupert L. Frank
 On the Laplacian in the halfspace with a periodic boundary condition
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Dec 9, 04

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Abstract. We study spectral and scattering properties of the Laplacian $H^{(\sigma)} = \Delta$ in $L_2(\R^{d+1}_+)$ corresponding to the boundary condition $\frac{\partial u}{\partial\nu} + \sigma u = 0$ with a periodic function $\sigma$. For nonnegative $\sigma$ we prove that $H^{(\sigma)}$ is unitarily equivalent to the Neumann Laplacian $H^{(0)}$. In general, there appear additional channels of scattering due to surface states. We prove absolute continuity of the spectrum of $H^{(\sigma)}$ under mild assumptions on $\sigma$.
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