The back-scattering problem in three dimensions

被引:6
|
作者
Lagergren, Robert [1 ]
机构
[1] Vaxjo Univ, Dept Math & Syst Engn, Vaxjo, Sweden
关键词
Schrodinger operator; Back-scattering; Inverse scattering;
D O I
10.1007/s11868-010-0021-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article we study the (inverse) back-scattering problem for the Schrodinger operator in R-3. We introduce the back-scattering transform B(upsilon) of a real-valued potential upsilon is an element of C-0(infinity) (R-3), and prove that the back-scattering data associated to v determine B(upsilon). Under the assumption that the Schrodinger operator H-upsilon = -Delta+v has no eigenvectors in L-2(R-3) it is shown that B(upsilon) may be expressed in terms of the wave group K-upsilon(t) = sin(t root H-upsilon)/root H-upsilon. We prove also that the mapping v bar right arrow B(upsilon) is a homeomorphism in a neighbourhood of the origin in the Banach space X-0(r), which is the completion of C-0(infinity) (R-3; R) w.r.t. the norm f bar right arrow Sigma(vertical bar a vertical bar=1) parallel to partial derivative(a) f parallel to L-1.
引用
收藏
页码:1 / 64
页数:64
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