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Inverse scattering for the 1-D Helmholtz equation

Ingrid Beltita·Renata Bunoiu
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Abstract

We prove a uniqueness result for Nevanlinna functions. and this result is then used to give an elementary proof of the uniqueness in the inverse scattering problem for the equation $ u" + \frac{k^2}{c^2}u=0 $ on $\mathbb R$. Here $c$ is a real positive measurable function that is bounded from below by a positive constant, and is close to $1$ at $\pm \infty$.

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Ingrid Beltita, Renata Bunoiu. 2005-11-16. Inverse scattering for the 1-D Helmholtz equation. https://arxiv.org/abs/math/0511401

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