Finite dimensional four spectra inverse problem |
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Author |
v.pivovarchik@paco.net
South Ukrainian National Pedagogical University
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Abstract |
We find necessary and suffcient conditions for four finite sequences of positive numbers to be
certain parts of spectra of the Dirichlet-Dirichlet, Dirichlet-Neumann, Neumann-Dirichlet and
Neumann-Neumann boundary value problems generated by the same Stieltjes string recurrence
relations.
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Keywords |
Lagrange identity; Stieltjes string; eigenvalues; continued fraction
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Reference |
1. V.A. Ambarzumian, Uber eine Frage der Eigenwerttheorie, Zeitschrift fur Physik, 53 (1929), 690–695.
2. G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math., 78 (1946), 1–96. 3. M. Horvath, On the inverse spectral theory of SrЁodinger and Dirac operators, Trans. Amer. Math. Soc., 353 (2001), №10, 4155–4171. 4. M. Horvath, Inverse spectral problems and closed exponential systems, Ann. of Math., 162 (2005), 885– 918. 5. F. Gesztesy, R. del Rio, B. Simon, Inverse spectral analysis with partial information on the potential. III. Updating boundary conditions, Int. Math. Res. Not. IMRN, 15 (1997), 751–758. 6. R.F. Gantmakher, M.G. Krein, Oscillation matrices and kernels and small vibrations of mechanical systems, GITTL, Moscow–Leningrad, 1950. (in Russian); German transl.: Akademie Verlag, Berlin, 1960. 7. C.-K. Law, V. Pivovarchik, W.C. Wang, Apolynomial identity and its application to inverse spectral problems in Stieltjes strings, to appear in Operators and Matrices. 8. V. Pivovarchik, An inverse problem by eigenvalues of four spectra, J. Math. Anal. Appl., 396 (2012), №2, 715–723. |
Pages |
73-80
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Volume |
41
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Issue |
1
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Year |
2014
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Journal |
Matematychni Studii
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Full text of paper | |
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