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
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.
@article{10_4171_dm_159,
author = {N. Filonov and F. Klopp},
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},
year = {2004},
volume = {9},
doi = {10.4171/dm/159},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/159/}
}
TY - JOUR AU - N. Filonov AU - F. Klopp TI - Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others JO - Documenta mathematica PY - 2004 SP - 107 EP - 121 VL - 9 UR - http://geodesic.mathdoc.fr/articles/10.4171/dm/159/ DO - 10.4171/dm/159 ID - 10_4171_dm_159 ER -
%0 Journal Article %A N. Filonov %A F. Klopp %T Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others %J Documenta mathematica %D 2004 %P 107-121 %V 9 %U http://geodesic.mathdoc.fr/articles/10.4171/dm/159/ %R 10.4171/dm/159 %F 10_4171_dm_159
N. Filonov; F. Klopp. 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. doi: 10.4171/dm/159
Cité par Sources :