Transmission eigenvalues

SIAM Journal on Mathematical Analysis

Volumn 40, Issue 2, 2008, Pages 738-753

  Päivärinta, Lassi ^a   Sylvester, John ^b  

^a UNIVERSITY OF HELSINKI   (Finland)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Helmholtz equation; Inverse problems; Inverse scattering; Transmission eigenvalues

Indexed keywords

INHOMOGENEOUS MEDIUMS; INVERSE SCATTERING; RADIAL SYMMETRIES; SAMPLING METHODS; SCATTERING OPERATORS; SCATTERING PROBLEMS; TIME HARMONICS; WAVE-NUMBERS;

DIFFERENTIAL EQUATIONS; HELMHOLTZ EQUATION; MATHEMATICAL OPERATORS; SCATTERING;

INVERSE PROBLEMS;

EID: 62649109684     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070697525     Document Type: Article

References (13)

1. S. AGMON, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa CI. Sci. (4), 2 (1975), pp. 151-218.
2. S. AGMON AND L. HÖRMANDER, Asymptotic properties of solutions of differential equations with simple characteristics, J. Anal. Math., 30 (1976), pp. 1-38.
3. F. CAKONI, D. COLTON, AND P. MONK, On the use of transmission eigenvalues to estimate the index of refraction from far field data, Inverse Problems, 23 (2007), pp. 507-522.
4. D. COLTON, A. KIRSCH, AND L. PÄIVARINTA, Far-field patterns for acoustic waves in an inho-mogeneous medium, SIAM J. Math. Anal., 20 (1989), pp. 1472-1483.
5. D. COLTON AND R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Appl. Math. Sci. 93, Springer-Verlag, Berlin, 1998.
6. D. COLTON AND P. MONK, The inverse scattering problem for acoustic waves in an inhomoge-neous medium, in Inverse Problems in Partial Differential Equations (Areata, CA, 1989), D. Colton, R. Ewing, and W. Rundell, eds., SIAM, Philadelphia, 1990, pp. 73-84.
7. D. COLTON, L. PAIVARINTA, AND J. SYLVESTER, The interior transmission problem, Inverse Probl. Imaging, 1 (2007), pp. 13-28.
8. L. HÖRMANDER, The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients, Classics in Mathematics, Springer-Verlag, Berlin, 2005.
9. J. R. MCLAUGHLIN AND P. L. POLYAKOV, On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues, J. Differential Equations, 107 (1994), pp. 351-382.
10. J. R. MCLAUGHLIN, P. L. POLYAKOV, AND P. E. SACKS, Reconstruction of a spherically symmetric speed of sound, SIAM J. Appl. Math., 54 (1994), pp. 1203-1223.
11. M. REED AND B. SIMON, Methods of Modern Mathematical Physics. I. Functional Analysis, 2nd ed., Academic Press, New York, 1980.
12. B. P. RYNNE AND B. D. SLEEMAN, The interior transmission problem and inverse scattering from inhomogeneous media, SIAM J. Math. Anal., 22 (1991), pp. 1755-1762.
13. B. SIMON, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton Series in Physics, Princeton University Press, Princeton, NJ, 1971.