Author:
Colton David,Sleeman Brian D.
Abstract
AbstractA 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.AMS 2000 Mathematics subject classification: Primary 35R30. Secondary 35P25
Publisher
Cambridge University Press (CUP)
Cited by
42 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A Universal Framework for Holographic MIMO Sensing;ICC 2024 - IEEE International Conference on Communications;2024-06-09
2. Inverse Acoustic Obstacle Scattering;Applied Mathematical Sciences;2019
3. Reciprocity gap method for an interior inverse scattering problem;Journal of Inverse and Ill-posed Problems;2017-01-01
4. The reciprocity gap method for a cavity in an inhomogeneous medium;Inverse Problems and Imaging;2016-08
5. Inverse Scattering;Handbook of Mathematical Methods in Imaging;2015