Numerical technique for the inverse resonance problem

Journal of Computational and Applied Mathematics

Volumn 171, Issue 1-2, 2004, Pages 337-347

  Rundell, William ^a   Sacks, Paul ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; RESONANCE;

EIGENPARAMETERS; JOST FUNCTION; RESONANCE PARAMETERS;

PROBLEM SOLVING;

MATHEMATICAL ANALYSIS;

EID: 3042636111     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.01.035     Document Type: Article

References (25)

1. T. Aktosun, Construction of the half-line potential from the Jost function, 2003, Preprint.
2. Binding P.A. A hierarchy of Sturm-Liouville problems Math. Methods Appl. Sci. 26 2003 349-357
3. Binding P.A. Browne P.J. Watson B.A. Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions J. London Math. Soc. (2) 62 1 2000 161-182
4. Binding P.A. Browne P.J. Watson B.A. Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. II J. Comput. Appl. Math. 148 1 2002 147-168
5. B.M. Brown, I. Knowles, R. Weikard, On the inverse resonance problem, 2003, Preprint.
6. Browne P.J. Sleeman B.D. Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions Inverse Problems 12 4 1996 377-381
7. Browne P.J. Sleeman B.D. A uniqueness theorem for inverse eigenparameter dependent Sturm-Liouville problems Inverse Problems 13 6 1997 1453-1462
8. Chadan K. Sabatier P. Inverse Problems in Quantum Scattering Theory 1989 Springer Berlin
9. Ching E.S.C. Leung P.T. Maasen van den Brink A. Suen W.M. Tong S.S. Young K. Quasinormal-mode expansion for waves in open systems Rev. Mod. Phys. 70 1998 1545-1554
10. Freiling G. Yurko V. Inverse Sturm-Liouville Problems and Their Applications 2001 Nova Science Publishers New York
11. Gelfand I.M. Levitan B.M. On the determination of a differential equation from its spectral function Amer. Math. Soc. Trans. 1 1951 253-304
12. Kravickii A.O. Double expansion into series of eigenfunctions of a certain nonself-adjoint boundary-value problem Differential Uravneniya 4 1968 165-177
13. B.M. Levitan, Inverse Sturm-Liouville Problems, VNU Science Press, Utrecht, 1987.
14. McCarthy C.M. Rundell W. Eigenparameter dependent inverse Sturm-Liouville problems Numer. Func. Anal. Optim. 24 1-2 2003 85-105
15. McLaughlin J.R. Polyakov P.L. On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues J. Differential Equations 107 2 1994 351-382
16. Newton R.G. Scattering Theory of Waves and Particles 1982 Springer Berlin
17. Pivovarchik V. van der Mee C. The inverse generalized Regge problem Inverse Problems 17 2001 1831-1845
18. Pöschel J. Trubowitz E. Inverse spectral theory Pure and Applied Mathematics Vol. 130 1987 Academic Press Inc. Boston, MA
19. Regge T. Analytic properties of the scattering matrix Nuovo Cimento 8 1958 671-679
20. Regge T. Construction of potentials from resonance parameters Nuovo Cimento 9 1958 491-503
21. Rundell W. Sacks P.E. Reconstruction techniques for classical inverse Sturm-Liouville problems Math. Comp. 58 1992 161-184
22. Sergeev A.G. The asymptotic behavior of the Jost function and of the eigenvalues of the Regge problem Differential Uravneniya 8 1972 925-927
23. van der Mee C. Pivovarchik V.N. An inverse Sturm-Liouville problem with boundary conditions depending on the spectral parameter Funktsional. Anal. i Prilozhen. 36 4 2002 74-77
24. Young R. An Introduction to Nonharmonic Fourier Series 1980 Academic Press New York
25. V. Yurko, Method of Spectral Mappings in the Inverse Problem Theory, VSP, Utrecht, 2002.