Analytic continuation and resonance-free regions for Sturm–Liouville potentials with power decay

摘要

The analytic continuation of the Jost solution into a sector of the unphysical sheet is established for analytic potentials with power decay. The method also yields resonance-free regions which, in the case of super-exponential decay, are confirmed to be the best possible of their kind by the known asymptotic distribution of resonances.