On the location of resonances of exponentially decaying Sturm–Liouville potentials

摘要

The paper is concerned with analytic continuation into the unphysical sheet for Sturm–Liouville potentials whose decay at infinity is no faster than O(e−ax). A resonance-free region is found and the existence of a natural boundary is discussed. An example related to the Bessel equation is examined in some detail.