Zeros of the Jost function for a class of exponentially decaying potentials
Date
2005-12-08
Authors
Gilbert, Daphne
Kerouanton, Alain
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Jost solution, Sturm-Liouville operators, Resonances, Eigenvalues, Spectral singularities
Citation
Gilbert, D., & Kerouanton, A. (2005). Zeros of the Jost function for a class of exponentially decaying potentials. <i>Electronic Journal of Differential Equations, 2005</i>(145), pp. 1-9.
Rights
Attribution 4.0 International