Geodesic
Zeros of the Jost function for a class of exponentially decaying potentials
Electronic journal of differential equations, Tome 2005 (2005)
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 $a$ and $c$.
Classification : 34L40, 35B34, 35P15, 33C10
Keywords: Jost solution, Sturm-Liouville operators, resonances, eigenvalues, spectral singularities 
@article{EJDE_2005__2005__a8,
     author = {Gilbert,  Daphne and Kerouanton,  Alain},
     title = {Zeros of the {Jost} function for a class of exponentially decaying potentials},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1095.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a8/}
}
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Gilbert,  Daphne; Kerouanton,  Alain. Zeros of the Jost function for a class of exponentially decaying potentials. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a8/