One-dimensional inverse scattering and spectral problems
| dc.creator | Ramm, Alexander G. | |
| dc.date | 2003-09-12 | |
| dc.date | 2003-09-14 | |
| dc.date.accessioned | 2026-07-07T04:30:32Z | |
| dc.date.available | 2026-07-07T04:30:32Z | |
| dc.description | Inverse 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.description | 102 pp | |
| dc.identifier | https://arxiv.org/abs/math-ph/0309028 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0309028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57498 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34B25, 35R30, 81F05, 81F90 | |
| dc.title | One-dimensional inverse scattering and spectral problems | |
| dc.type | text |