Rupert L. Frank

摘要

We study spectral and scattering properties of the Laplacian $H^{(sigma)} = -Delta$ in $L_2(R^2_+)$ corresponding to the boundary condition $rac{partial u}{partialu} + sigma u = 0$ for a wide class of periodic functions $sigma$. The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators $W_pm(H^{(sigma)},H^{(0)})$ exist.