Zeros of the Jost function for a class of exponentially decaying potentials
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We investigate the properties of a series representing the Jost solution for the differential equation -y′′ + q(x)y = λy, x ≥ 0, q ∈ L(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)| ≤ ce-αx, x ≥ 0, for some α > 0, and c > 0.
CitationGilbert, D., & Kerouanton, A. (2005). Zeros of the Jost function for a class of exponentially decaying potentials. Electronic Journal of Differential Equations, 2005(145), pp. 1-9.
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