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.