Geodesic
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering
Documenta mathematica, Tome 9 (2004), pp. 57-77
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We study spectral and scattering properties of the Laplacian H(σ)=−Δ in L2​(R+2​) corresponding to the boundary condition ∂ν∂u​+σu=0 for a wide class of periodic functions σ. For non-negative σ we prove that H(σ) is unitarily equivalent to the Neumann Laplacian H(0). In general, there appear additional channels of scattering which are analyzed in detail.
DOI : 10.4171/dm/157
Classification : 35J10, 35J25, 35P05, 35P25
Mots-clés : Schrödinger operator, singular potential, scattering theory, periodic operator 
@article{10_4171_dm_157,
     author = {Roman G. Shterenberg and Rupert L. Frank},
     title = {On the scattering theory of the {Laplacian} with a periodic boundary condition. {II.} {Additional} channels of scattering},
     journal = {Documenta mathematica},
     pages = {57--77},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/157},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/157/}
}
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Roman G. Shterenberg; Rupert L. Frank. On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Documenta mathematica, Tome 9 (2004), pp. 57-77. doi: 10.4171/dm/157

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