The d-bar approach to approximate inverse scattering at fixed energy in three dimensions
| dc.creator | Novikov, Roman | |
| dc.date | 2005-05-10 | |
| dc.date.accessioned | 2026-07-07T06:26:16Z | |
| dc.date.available | 2026-07-07T06:26:16Z | |
| dc.description | We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from its scattering amplitude $f$ at fixed energy $E>0$ in dimension $d=3$. In particular, in three dimensions we stably reconstruct n-times smooth potential $v$ with sufficient decay at infinity, $n>3$, from its scattering amplitude $f$ at fixed energy $E$ up to $O(E^{-(n-3-ε)/2})$ in the uniform norm as $E\to +\infty$ for any fixed arbitrary small $ε>0$ (that is with almost the same decay rate of the error for $E\to +\infty$ as in the linearized case near zero potential). | |
| dc.identifier | https://arxiv.org/abs/math-ph/0505033 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0505033 | |
| dc.identifier | International Mathematics Research Papers 2005:6 (2005) 287-349 | |
| dc.identifier | doi:10.1155/IMRP.2005.287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97059 | |
| dc.subject | Mathematical Physics | |
| dc.title | The d-bar approach to approximate inverse scattering at fixed energy in three dimensions | |
| dc.type | text |