Weyl-function asymptotics with applications to PT-symmetry and point interactions

Weyl m -function characterisations can be used to describe the behaviour of eigenvalues of Schrödinger operators with point interactions. Using complex scaling, transformators and a local Borg-Marchenko theorem we describe the asymptotic behaviour of m(λ ) m ( λ ) as |λ |→ ∞ | λ | → ∞ in different regions of C C . Our asymptotic results are applied to the evolution of real eigenvalues of δ δ and δ ' δ ′ perturbations of PT P T -symmetric problems as functions of coupling constants.