Geodesic
On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 78-95

Voir la notice de l'article provenant de la source Math-Net.Ru

Absolute continuity of the spectrum of a two-dimensional generalized periodic Schrödinger operator with continuous metric $g$ and scalar potential $V$ is proved provided that the Fourier coefficients of the functions $g^{\pm 1/2}$ satisfy the condition $\sum |N|^{1/2}|(g^{\pm 1/2})_N|+\infty $ and the scalar potential $V$ has relative bound zero with respect to the operator $-\Delta $ in the sense of quadratic forms.
Keywords: generalized Schrödinger operator, absolute continuity of the spectrum, periodic potential. 
@article{IIMI_2013_41_1_a2,
     author = {L. I. Danilov},
     title = {On the spectrum of a two-dimensional generalized periodic {Schr\"odinger} operator},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {78--95},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a2/}
}
TY  - JOUR
AU  - L. I. Danilov
TI  - On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2013
SP  - 78
EP  - 95
VL  - 41
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a2/
LA  - ru
ID  - IIMI_2013_41_1_a2
ER  - 
%0 Journal Article
%A L. I. Danilov
%T On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2013
%P 78-95
%V 41
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a2/
%G ru
%F IIMI_2013_41_1_a2
L. I. Danilov. On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 78-95. http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a2/