On the reconstruction of a string from spectral data

Mathematische Nachrichten

Volumn 197, Issue , 1999, Pages 135-156

  Weber, Matthias ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Inverse eigenvalue problem; Krein's correspondence; Moment problems; Vibrating string

Indexed keywords

EID: 0007323476     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19991970109     Document Type: Article

References (23)

1. AKHIEZER, N. I.: The Classical Moment Problem and Some Related Questions in Analysis, Oliver & Boyd, Edinburgh and London, 1965
2. BARCILON, V.: Explicit Solution of the Inverse Problem for a Vibrating String, J. Math. Anal. Appl. 93 (1983), 222-234
3. BRAUN, S. G., and RAM, Y. M.: Structural Parameter Identification in the Frequency Domain: The Use of Overdetermined Systems, J. Dynamic Systems, Measurement and Control 109 (1987), 120-123
4. DYM, H., and McKEAN, H. P.: Gaussian Processes, Function Theory and the Inverse Spectral Problem, Academic Press, New York, 1976
5. DYNKIN, E. B.: Markov Processes, Springer - Verlag, Berlin, 1965
6. GANTMAKHER, F. P., and KREIN, M. G.: Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems (Russian), State Publishing House of Technical - Theoretical Literature, Moscow, Leningrad, 1961
7. GLADWELL. G. M. L.: Inverse Problems in Vibration, Nijhoff, Dortrecht, 1986
8. CLADWELL, G. M, L., and GBADEYAN, J. A.: On the Inverse Problem of the Vibrating String or Rod, Q. J. Mech. Appl. Math, 38 (1985), 169-174
9. HOCHSTADT, H,: On the Determination of the Density of a Vibrating String from Spectral Data, J. Math. Anal. Appl. 55 (1976), 673-685
10. KAC, I. S.: The Spectral Theory of the String (Russian), Ukrain. Mat. Z. 46 (1994), 155-176
11. KAC, I. S., and KREIN, M. G.: On the Spectral Function of the String, Amer. Math. Soc. Transl. (2), 103 (1974), 19-102
12. KASAHARA, Y.: Spectral Theory of Strings and Generalized Diffusion Processes, Japan J. Math. 1 (1975), 67-84
13. KOTANI, S., and WATANABE, S.: Krein's Spectral Theory of Strings and Generalized Diffusion Processes, in Functional Analysis in Markov Processes, M. FUKUSHIMA, ed., LNM 923, 235-259, Springer - Verlag, Berlin, Heidelberg, New York, 1982
14. KREIN, M. G.: Determination of the Density of a Non - Homogeneous Symmetric Cord from Its Frequency Spectrum (Russian), Dokl. Akad. Nauk SSSR (N. S.) 76 (1951), 345-348
15. KREIN, M. G.: On the Inverse Problem for a Non - Homogeneous Cord (Russian), Dokl. Akad. Nauk SSSR (N.S.) 82 (1951), 669-672
16. KREIN, M. G.: Some New Problems in the Theory of Sturm Systems (Russian), Prikl. Matem. Mekh. 16 (1952), 555-563
17. CHAR. B. W.. GEDDES, K. O., GONNET, G. H., LEONG, B. L., MONAGAN, M. B., and WATT. S. M.: Maple V Language Reference Manual, Springer Verlag. New York, 1991
18. MAKCHENKO, V. A.: On Certain Questions in the Theory of Differential Operators of Second Order (Russian), Dokl. Akad. Nauk SSSR, 72 (1950), 457-460
19. PERRON, O.: Die Lehre von den Kettenbrüchen, B. G. Teubner, Leipzig, Berlin, 1929
20. POLYA, G., and SZEGÖ, G.: Aufgaben und Lehrsätze aus der Analysis, Springer - Verlag, Berlin, Göttingen, Heidelberg, New York, 1964
21. RAM. Y. M.: Inverse Eigenvalue Problem for a Modified Vibrating System, SIAM Appl. Math. 53 (1993), 1762-1775
22. RAM, Y. M., and CALDWELL. J.: Physical Parameter Reconstruction of a Free Free Mass -Spring System from Its Spectra, SIAM Appl. Math. 52 (1992), 140-152
23. WALL, H. S.: Analytic Theory of Continued Fractions, D. van Nostrand, Toronto, New York, London, 1948