Geodesic
Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others
Documenta mathematica, Tome 9 (2004), pp. 107-121.

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

Summary: We prove that the spectrum of a Schrödinger operator with a potential which is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous. Therefore, we reduce the operator using the Bloch-Floquet-Gelfand transform in the periodic variables, and show that, except for at most a set of quasi-momenta of measure zero, the reduced operators satisfies a limiting absorption principle.
Classification : 35J10, 35Q40, 81C10 
@article{DOCMA_2004__9__a23,
     author = {Filonov, N. and Klopp, F.},
     title = {Absolute continuity of the spectrum of a {Schr\"odinger} operator with a potential which is periodic in some directions and decays in others},
     journal = {Documenta mathematica},
     pages = {107--121},
     publisher = {mathdoc},
     volume = {9},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a23/}
}
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Filonov, N.; Klopp, F. Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others. Documenta mathematica, Tome 9 (2004), pp. 107-121. http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a23/