Document Type

Article

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This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Publication Details

Electronic journal of differential equations, Vol. 2005 (2005), No. 145. pp 109

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 $c$ greator than 0.

DOI

https://doi.org/10.1016/j.jfa.2006.03.025


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