Perturbations of a one-dimensional Schrödinger operator with limit- periodic potential (Q1071923)

The author investigates the Schrödinger operator \[ H=-(d^ 2/dx^ 2)+\sum^{\infty}_{n=0}a_ n \cos (x/2^ n)+V(x),\quad x\in R, \] in \(L_ 2(R)\), where \(V\in L_ 1(R)\cap L_ 2(R)\). Under certain assumptions on the coefficients of the sequence \(\{a_ n\}\) the spectrum of the operator H is investigated. Moreover it is proved that the continuous singular spectrum of the operator H is an empty set.