Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory

Inverse Problems

Volumn 15, Issue 2, 1999, Pages 413-429

  Kirsch, Andreas ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001119601     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/15/2/005     Document Type: Article

References (14)

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4. Colton D and Monk P 1998 A linear sampling method for the detection of leukemia using microwaves SIAM J. Appl. Math. 58 926-41
5. Colton D, Piana M and Potthast R 1997 A simple method using Morozov's discrepancy principle for solving inverse scattering problems Inverse Problems 13 1447-93
6. Gilbarg D and Trudinger N S 1977 Elliptic Partial Differential Equations of Second Order (Berlin: Springer)
7. Günter N M 1957 Die Potentialtheorie und Ihre Anwendungen auf Grundaufgaben der Mathematischen Physik (Leipzig: Teubner)
8. Kersten H 1980 Grenz-und Sprungrelationen für potentiale mit quadratsummierbarer dichte Resultate D. Math. 3 17-24
9. Kirsch A 1992 Remarks on some notions of weak solutions for the Helmholtz equation Appl. Anal. 47 7-24
10. Kirsch A 1996 An Introduction to the Mathematical Theory of Inverse Problems (Berlin: Springer)
11. Kirsch A 1998 Characterization of the shape of the scattering obstacle by the spectral data of the far-field operator Inverse Problems 14 1489-512
12. Ringrose J R 1971 Compact Non-Self-Adjoint Operators (London: Van Nostrand Reinhold)
13. Rynne B P and Sleeman B D 1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-62
14. Tikhonov A N, Goncharsky A V, Stepanov V V and Yagola A G 1995 Numerical Methods for the Solution of Ill-posed Problems (Dordrecht: Kluwer)