On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator

L. I. Danilov

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 78-95.

Résumé

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.

Détail

Keywords: generalized Schrödinger operator, absolute continuity of the spectrum, periodic potential.

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