Geodesic
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
Documenta mathematica, Tome 8 (2003), pp. 547-565.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study spectral and scattering properties of the Laplacian $H^{(\sigma)} = -\Delta$ in $L_2(\R^2_+)$ 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 an unbounded cell which are analyzed in detail. We prove that the wave operators $W_\pm(H^{(\sigma)},H^{(0)})$ exist.
Classification : 35J10, 35J25, 35P05, 35P25
Keywords: scattering theory, periodic operator, Schrödinger operator, singular potential 
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     author = {Frank, Rupert L.},
     title = {On the scattering theory of the {Laplacian} with a periodic boundary condition. {I.} {Existence} of wave operators},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a3/}
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Frank, Rupert L. On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Documenta mathematica, Tome 8 (2003), pp. 547-565. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a3/