The Borg-Marchenko Theorem with a Continuous Spectrum
| dc.creator | Aktosun, Tuncay | |
| dc.creator | Weder, Ricardo | |
| dc.date | 2005-12-01 | |
| dc.date.accessioned | 2026-07-07T06:54:35Z | |
| dc.date.available | 2026-07-07T06:54:35Z | |
| dc.description | The Schrödinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result provides a generalization of the celebrated uniqueness theorem of Borg and Marchenko using two sets of discrete spectra to the case where there is also a continuous spectrum. The proof employed yields a method to recover the potential and the two boundary conditions, and it also constructs data sets used in various inversion methods. A comparison is made with the uniqueness result of Gesztesy and Simon using Krein's spectral shift function as the inversion data. | |
| dc.description | To appear in the proceedings of the 2005 UAB International Conference on Differential Equations and Mathematical Physics | |
| dc.identifier | https://arxiv.org/abs/math-ph/0512001 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0512001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105989 | |
| dc.subject | Mathematical Physics | |
| dc.title | The Borg-Marchenko Theorem with a Continuous Spectrum | |
| dc.type | text |