An approximation property of importance in inverse scattering theory

被引：18

作者：

Colton, D ^{[1
]}

Sleeman, BD

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2001年 / 44卷

关键词：

inverse obstacle scattering; Herglotz wave functions; the linear sampling method;

D O I：

10.1017/S0013091500000626

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A key step in establishing the validity of the linear sampling method of determining an unknown scattering obstacle D from a knowledge of its far-field pattern is to prove that solutions of the Helmholtz equation in D can be approximated in H-1(D) by Herglotz wave functions. To this end we establish the important property that the set of Herglotz wave functions is dense in the space of solutions of the Helmholtz equation with respect to the Sobolev space H-1(D) norm.

引用

页码：449 / 454

页数：6

共 9 条

[1] A simple method for solving inverse scattering problems in the resonance region [J].