Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H) (Q1122766)

The authors study the eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H). In particular, they consider questions of asymptotic distributions of eigenvalues and bounds on the number of branches. They study the asymptotics for \(N_-\) (eigenvalue distribution function) for \(W\geq 0\) and \(W(x)\sim c| x|^{- \alpha}\) as \(| x| \to \infty\), in the case where W is supported in a finite ball, and where \(W=W_+-W_-\) with \(W_{\pm}\geq 0\).