Using relative oscillation theory and the reducible result of Eliasson studied perturbations of quasiperiodic Schrödinger operators.
Let be a -dimensional torus, where . Let be a real analytic function. The Schrödinger operator on is given by
where is fixed. The author investigates decaying perturbations of the quasiperiodic operator . That is, he considers the operator
for some function . Assume that as , and let , , be a boundary point of the essential spectrum of ( is a certain constant). Then
for open sets and there exists a constant such that is an accumulation point of eigenvalues of if
and is not an accumulation point of eigenvalues of
Also, similar results are given for the operator , where .