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Property C for ordinary differential equations and applications to inverse scattering. (English) Zbl 0935.35177

Summary: 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 problems 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.

MSC:

35R30 Inverse problems for PDEs
34L25 Scattering theory, inverse scattering involving ordinary differential operators
35P25 Scattering theory for PDEs
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References:

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