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

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.