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AN APPROXIMATION PROPERTY OF IMPORTANCE IN INVERSE SCATTERING THEORY

Published online by Cambridge University Press:  20 January 2009

David Colton  and
Brian D. Sleeman
David Colton
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Brian D. Sleeman
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
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Abstract

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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.

AMS 2000 Mathematics subject classification: Primary 35R30. Secondary 35P25

Keywords

inverse obstacle scatteringHerglotz wave functionsthe linear sampling method
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 3 , October 2001 , pp. 449 - 454
Copyright
Copyright © Edinburgh Mathematical Society 2001