Electron. J. Diff. Eqns., Vol. 2005(2005), No. 145, pp. 1-9.

Zeros of the Jost function for a class of exponentially decaying potentials

Daphne Gilbert, Alain Kerouanton

Abstract:
We investigate the properties of a series representing the Jost solution for the differential equation $-y''+q(x)y=\lambda y$, $x \geq 0$, $q \in L({\mathbb{R}}^{+})$. 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 $a$ greater than 0 and $c$ greater than 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.

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Daphne Gilbert
School of Mathematical Sciences
Dublin Institute of Technology
Kevin Street, Dublin 8, Ireland
email: daphne.gilbert@dit.ie
Alain Kerouanton
School of Mathematical Sciences
Dublin Institute of Technology
Kevin Street, Dublin 8, Ireland
email: alainkerouanton@hotmail.com   Fax: +35314024994

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