Local smoothing for the backscattering transform
| dc.creator | Beltita, Ingrid | |
| dc.creator | Melin, Anders | |
| dc.date | 2007-12-22 | |
| dc.date.accessioned | 2026-07-07T08:51:08Z | |
| dc.date.available | 2026-07-07T08:51:08Z | |
| dc.description | An analysis of the backscattering data for the Schrödinger operator in odd dimensions $n\ge 3$ motivates the introduction of the backscattering transform $B: C_0^\infty ({\mathbb R}^n;{\mathbb C})\to C^\infty ({\mathbb R}^n; {\mathbb C})$. This is an entire analytic mapping and we write $ Bv = \sum_1^\infty B_Nv $ where $B_Nv$ is the $N$:th order term in the power series expansion at $v=0$. In this paper we study estimates for $B_Nv$ in $H_{(s)}$ spaces, and prove that $Bv$ is entire analytic in $v \in H_{(s)}\cap \Cal E'$ when $s\ge (n-3)/2$. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0712.3865 | |
| dc.identifier | http://arxiv.org/abs/0712.3865 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144833 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81U40; 35R30 | |
| dc.title | Local smoothing for the backscattering transform | |
| dc.type | text |