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On the spectrum of a two-dimensional generalized periodic Schrödinger operator

L. I. Danilov

Physical Technical Institute, Ural Branch of the Russian Academy of Sciences, ul. Kirova, 132, Izhevsk, 426000, Russia

Abstract: 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.

UDC: 517.958+517.984.5

MSC: 35P05

Received: 15.01.2013

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