Stability of an inverse problem in potential scattering on the real line

Communications in Partial Differential Equations

Volumn 25, Issue 5-6, 2000, Pages 925-955

  Hitrik, Michael ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034364975     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300008821537     Document Type: Article

References (20)

1. G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172.
2. P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), 121-251.
3. L. D. Faddeev, Inverse problem of quantum theory of scattering II, J. Sov. Math. 5(1) (1976), 334-396.
4. J. Garnett, Bounded analytic functions, Academic Press, New York, 1981.
5. A. A. Gonchar, G. M. Henkin, and N. N. Novikova, Multipoint Padé approximants in an inverse Sturm-Liouville problem. (Russian) Mat. Sb. 182, no.8 (1991), 1118-1128.
6. English translation in Math. USSR Sbornik 73, no. 2 (1992), 479-489.
7. P. Grisvard, Elliptic problems in non-smooth domains, Pitman Publishing, Boston, 1983.
8. M. Hitrik, Bounds on scattering poles in one dimension, preprint, 1998.
9. L. Hörmander, Notions of convexity, Birkhäuser, Boston, 1994.
10. V. Isakov, Uniqueness and stability in multi-dimensional inverse problem, Inverse Problems 6 (1993), 579-621.
11. J. Lee and G. Uhlmann, Determining anisotropic real-analytic conductivities by boundary measurements, Comm. Pure Appl. Math. 42 (1989), 1097-1112.
12. V. A. Marchenko, Sturm-Liouville operators and applications, Birkhäuser Verlag, Basel, 1986.
13. V. M. Markushevich and N. N. Novikova, On the uniqueness of the solution of inverse scattering problem on the real axis for the potentials placed on the positive half-axis, Comput. Seismology 18 (1985), p. 176-184 (Russian).
14. A. Melin, Operator methods for inverse scattering on the real line, Comm. P.D.E. 10 (1985), 677-766.
15. A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. Math. 142 (1996), 71-96.
16. A. G. Ramm, Stability estimates in inverse scattering, Acta Appl. Math. 28 (1992), 1-42.
17. P. Stefanov, Stability of the inverse problem in potential scattering at fixed energy, Ann. Inst. Fourier 40 (1990), 867-884.
18. J. Sylvester, A convergent layer stripping algorithm for the radially symmetric impedance tomography problem, Comm. P.D.E. 17 (1992), 1955-1994.
19. G. Uhlmann, Inverse boundary problems and applications, Asterisque 207 (1992), 153-211.
20. G. Uhlmann, Inverse boundary value problems for partial differential equations, Doc. Math. J. DMV Extra volume ICM III (1998), 77-86.