Structure of the spectrum of the periodic Schrödinger operator on the Euclidean torus (Q1067589)

The paper refers to the adjoint Schrödinger operator \(H_ t=-\Delta +q(x)\) in \(L^ 2(T^{\nu})\), where \(T^{\nu}\) is an euclidean torus, q(x) an enough smooth potential and with boundary conditions: \(u(x+\omega_ j)=\exp \{it_ j\}u(x)\), \(t_ j\in [0,1]\), \(j=\overline{1,\nu}\), \(t=\sum_{j}t_ j\gamma^ j\). The paper completes two previous papers by the same authors: \textit{O. A. Veliev}, Dokl. Akad. Nauk SSSR 268, 1289-1292 (1983; Zbl 0541.47017) and \textit{S. A. Molchanov} and \textit{M. V. Novitski}, Usp. Mat. Nauk 38, No.5, 135-136 (1983).