One-dimensional inverse scattering and spectral problems

dc.creatorRamm, Alexander G.
dc.date2003-09-12
dc.date2003-09-14
dc.date.accessioned2026-07-07T04:30:32Z
dc.date.available2026-07-07T04:30:32Z
dc.descriptionInverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained 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: Analysis of the invertibility of the steps in the Gel'fand-Levitan and Marchenko inversion procedures, Theory of the inverse problem with I-function as the data and its applications; Proof of the property C for ordinary differential operators, numerous applications of property C; Inverse problems with "incomplete" data; 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. Complete presentation of the Krein inverse scattering theory is given. Consistency of this theory is proved. Quarkonium systems; Some new inverse problems for the heat and wave equations. A study of inverse scattering problem for an inhomogeneous Schrödinger equation;
dc.description102 pp
dc.identifierhttps://arxiv.org/abs/math-ph/0309028
dc.identifierhttp://arxiv.org/abs/math-ph/0309028
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57498
dc.subjectMathematical Physics
dc.subject34B25, 35R30, 81F05, 81F90
dc.titleOne-dimensional inverse scattering and spectral problems
dc.typetext

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