About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 713654, 6 pages
http://dx.doi.org/10.1155/2013/713654
Research Article

A Uniqueness Theorem for Bessel Operator from Interior Spectral Data

1Department of Mathematics, Faculty of Science and Art, Erzincan University, 24100 Erzincan, Turkey
2Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey

Received 24 February 2013; Accepted 12 April 2013

Academic Editor: Rodrigo Lopez Pouso

Copyright © 2013 Murat Sat and Etibar S. Panakhov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Borg, “Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte,” Acta Mathematica, vol. 78, pp. 1–96, 1946. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. V. A. Ambarzumyan, “Über eine frage der eigenwerttheorie,” Zeitschrift Für Physik, vol. 53, pp. 690–695, 1929.
  3. N. Levinson, “The inverse Sturm-Liouville problem,” Mathematica Tidsskrift B, vol. 1949, pp. 25–30, 1949. View at Zentralblatt MATH · View at MathSciNet
  4. B. M. Levitan, “On the determination of the Sturm-Liouville operator from one and two spectra,” Mathematics of the USSR-Izvestiya, vol. 12, pp. 179–193, 1978.
  5. H. Hochstadt, “The inverse Sturm-Liouville problem,” Communications on Pure and Applied Mathematics, vol. 26, pp. 715–729, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. A. Marchenko, “Certain problems of the theory of one dimensional linear di¤erential operators of the second order,” Trudy Moskovskogo Matematicheskogo Obshchestva, vol. 1, pp. 327–340, 1952.
  7. R. Carlson, “A Borg-Levinson theorem for Bessel operators,” Pacific Journal of Mathematics, vol. 177, no. 1, pp. 1–26, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. V. V. Stashevskaya, “On inverse problems of spectral analysis for a certain class of differential equations,” Doklady Akademii Nauk SSSR, vol. 93, pp. 409–412, 1953.
  9. S. Albeverio, R. Hryniv, and Ya. Mykytyuk, “Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra,” Methods of Functional Analysis and Topology, vol. 13, no. 2, pp. 110–123, 2007. View at MathSciNet
  10. G. Freiling and V. Yurko, “Inverse problems for differential operators with singular boundary conditions,” Mathematische Nachrichten, vol. 278, no. 12-13, pp. 1561–1578, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. V. A. Yurko, “On the reconstruction of Sturm-Liouville differential operators with singularities inside the interval,” Matematicheskie Zametki, vol. 64, no. 1, pp. 143–156, 1998, English translation in Mathematical Notes, vol. 64, no.1, pp. 121–132, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  12. V. A. Yurko, “An inverse problem for differential equations with a singularity,” Differentsial'nye Uravneniya, vol. 28, no. 8, pp. 1355–1362, 1992 (Russian), English translation in Differential Equations, vol. 28, pp. 1100–1107, 1992. View at MathSciNet
  13. V. A. Yurko, “On higher-order differential operators with a singular point,” Inverse Problems, vol. 9, no. 4, pp. 495–502, 1993. View at Zentralblatt MATH · View at MathSciNet
  14. F. Gesztesy and B. Simon, “Inverse spectral analysis with partial information on the potential. II. The case of discrete spectrum,” Transactions of the American Mathematical Society, vol. 352, no. 6, pp. 2765–2787, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. E. S. Panakhov and M. Sat, “On the determination of the singular Sturm-Liouville operator from two spectra,” CMES. Computer Modeling in Engineering & Sciences, vol. 84, no. 1, pp. 1–11, 2012. View at MathSciNet
  16. K. Mochizuki and I. Trooshin, “Inverse problem for interior spectral data of the Sturm-Liouville operator,” Journal of Inverse and Ill-Posed Problems, vol. 9, no. 4, pp. 425–433, 2001. View at Zentralblatt MATH · View at MathSciNet
  17. C.-F. Yang and X.-P. Yang, “An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions,” Applied Mathematics Letters, vol. 22, no. 9, pp. 1315–1319, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. G. A. Watson, Treatise on the Theory of the Bessel Functions, Cambridge University Press, Cambridge, UK, 1962.
  19. H. Koyunbakan, “Inverse spectral problem for some singular differential operators,” Tamsui Oxford Journal of Mathematical Sciences, vol. 25, no. 3, pp. 277–283, 2009. View at Zentralblatt MATH · View at MathSciNet
  20. W. Rundell and P. E. Sacks, “Reconstruction of a radially symmetric potential from two spectral sequences,” Journal of Mathematical Analysis and Applications, vol. 264, no. 2, pp. 354–381, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. V. Ya. Volk, “On inversion formulas for a differential equation with a singularity at x=0,” Uspekhi Matematicheskikh Nauk, vol. 8, no. 4, pp. 141–151, 1953. View at MathSciNet
  22. B. Ja. Levin, Distribution of Zeros of Entire Functions, vol. 5, American Mathematical Society, Providence, RI, USA, 1964. View at MathSciNet