Jacobi operators with singular continuous spectrum (Q1777321)

The author shows that for two classes of pairs of sequences \((c(n),v(n))\), the operator \(H\) acting on \(l^2(Z)\) by \((Hu)(n)=c(n)u(n+1)+ \overline{c(n-1)}u(n-1)+ v(n)u(n)\) has no eigenvalues. Applying these results to a class of quasiperiodic operators of magnetic origin, he shows, that in a region where a pure point spectrum is established for almost every phase and frequency, the operator has a pure singular continuous spectrum for a dense \(G_{\delta }\) in phase and a dense \(G_{\delta }\) in frequency. This is a generalisation of similiar results obtained for the Schrödinger operator.