Property C, that is, completeness of the set of products of some solutions to Sturm-Liouville equations is proved. Several uniqueness theorems for various inverse scattering prob-lems are obtained in a very simple way with the help of property C. Two classical uniqueness results for inverse scattering problem on the half-axis and for the inverse spectral problem are proved in a very short new way. Earlier the author introduced property C for partial differential equations and used it extensively for proving uniqueness theorems for many inverse problems.
Cite this article
A.G. Ramm, Property C for Ordinary Differential Equations and Applications to Inverse Scattering. Z. Anal. Anwend. 18 (1999), no. 2, pp. 331–348DOI 10.4171/ZAA/885