Anderson localization in the nondiscrete maryland model

The Schrödinger operator $H=H_0+V$, is considered where $V$ is an almost periodic potential of point interactions and the Hamiltonian $H_0$ is subject to certain conditions satisfied, in particular, by two- and three-dimensional operators of the form $H_0=-\Delta$ and $H_0=(i\nabla-\mathbf{A})^2$ $\mathbf{A}$ being a vector-potential of a uniform magnetic field. It is proved that under certain conditions of incommensurability for $V$, non-degenerate localised states of the operator $H$ are dense in forbidden bands of $H_0$; the expressions for corresponding eigen-functions are found.