Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 145, pp. 1-9.

Title: Zeros of the Jost function for a class of exponentially 
       decaying potentials
       
Authors: Daphne Gilbert (Dublin Institute of Technology, Ireland)
         Alain Kerouanton (Dublin Institute of Technology, Ireland)

Abstract: 
 We investigate the properties of a series representing the Jost
 solution for the differential equation $-y''+q(x)y=\lambda y$,
 $x \geq 0$, $q \in \mathrm{L}({\mathbb{R}}^{+})$.
 Sufficient conditions are determined on the real or complex-valued
 potential $q$ for the series to converge and bounds are obtained
 for the sets of eigenvalues, resonances and spectral singularities
 associated with a corresponding class of Sturm-Liouville operators.
 In this paper, we restrict our investigations to the class of
 potentials $q$ satisfying $|q(x)| \leq ce^{-ax}$, $x \geq 0$,
 for some $a>0$ and $c>0$.
 
Submitted October 4, 2005. Published December 8, 2005.
Math Subject Classifications: 34L40, 35B34, 35P15, 33C10.
Key Words: Jost solution; Sturm-Liouville operators;
           resonances; eigenvalues; spectral singularities.