One-dimensional inverse scattering and spectral problems.

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Show simple item record Ramm, Alexander G. 2011-06-03T15:59:57Z 2011-06-03T15:59:57Z 2011-06-03
dc.description.abstract Inverse scattering and spectral one-dimensional problems are discussed systematically in a selfcontained way. Many novel results due to the author are presented. The classical results are often presented in a new way. Several highlights of the new results include: 1) Analysis of the invertibility of the steps in the Gel’fand-Levitan and Marchenko inversion procedures, 2) Theory of the inverse problem with I-function as the data and its applications; 3) Proof of the property C for ordinary differential operators, numerous applications of property C; 4) Inverse problems with “incomplete” data; 5) Spherically symmetric inverse scattering problem with fixed-energy data: analysis of the Newton- Sabatier (NS) scheme for inversion of fixed-energy phase shifts is given. This analysis shows that the NS scheme is fundamentally wrong, and is not a valid inversion method. 6) Complete presentation of the Krein inverse scattering theory is given. Consistency of this theory is proved. 7) Quarkonium systems; 8) A study of the properties of I-function; 9) Some new inverse problems for the heat and wave equations are studied. 10) A study of inverse scattering problem for an inhomogeneous Schr¨odinger equation; en_US
dc.relation.uri en_US
dc.rights Permission to archive granted by editor, April 27, 2011. en_US
dc.subject Property C for ODE en_US
dc.subject Inverse spectral and scattering problems en_US
dc.subject Inverse problems for PDE and ODE en_US
dc.subject Spectral and scattering theory en_US
dc.title One-dimensional inverse scattering and spectral problems. en_US
dc.type Article (author version) en_US 2004 en_US
dc.citation.epage 426 en_US
dc.citation.issue 1 en_US
dc.citation.jtitle CUBO, A Mathematical Journal en_US
dc.citation.spage 313 en_US
dc.citation.volume 6 en_US
dc.contributor.authoreid ramm en_US

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