Property C for Ordinary Differential Equations and Applications to Inverse Scattering | Zendy

A. G. Ramm | Zendy

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Property C for Ordinary Differential Equations and Applications to Inverse Scattering

Author(s) -

A. G. Ramm

Publication year - 1999

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/885

Subject(s) - inverse scattering transform , ordinary differential equation , property (philosophy) , inverse , inverse scattering problem , mathematical analysis , mathematics , differential equation , inverse problem , geometry , philosophy , epistemology

Property C, that is, completeness of the set of products of some solutions to SturmLiouville 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.

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