Recovering asymptotics of Coulomb-like potentials from fixed energy scattering data

被引:7
|
作者
Joshi, MS [1 ]
机构
[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB2 1SB, England
关键词
scattering theory; Coulomb-like potentials; Lagrangian;
D O I
10.1137/S003614109732763X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Any compact smooth manifold, X, with boundary admits a Riemannian metric of the form x(?4)dx(2) + x(-2) h' near the boundary with x a boundary defining function and h' restricting to a metric on the boundary. Melrose [Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces, in Spectral and Scattering Theory, M. Ikawa, ed., Marcel Dekker, New York, 1994] has associated a scattering matrix to such metrics and potentials in xC(infinity) (X). It is shown for potentials of the form Ax + O(x(2)) that this scattering matrix is a Fourier integral operator and that the asymptotics of such potentials can be recovered from the scattering matrix for various manifolds including Euclidean space.
引用
收藏
页码:516 / 526
页数:11
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