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Retracted

This article has been retracted as it is essentially identical in content with the published article “Determination of Sturm-Liouville operator on a three-star graph from four spectra,” by I. Dehghani Tazehkand and A. Jodayree Akbarfam and published in Acta Universitatis Apulensis No. 32/2012, pp.147-172.

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References

  1. I. Dehghani Tazehkand and A. J. Akbarfam, “An inverse spectral problem for the Sturm-Liouville operator on a three-star graph,” ISRN Applied Mathematics, vol. 2012, Article ID 132842, 23 pages, 2012.
ISRN Applied Mathematics
Volume 2012, Article ID 132842, 23 pages
http://dx.doi.org/10.5402/2012/132842
Research Article

An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

Faculty of Mathematical Sciences, University of Tabriz, 29 Bahman Boulevard, Tabriz, Iran

Received 10 January 2012; Accepted 15 March 2012

Academic Editor: D. Georges

Copyright © 2012 I. Dehghani Tazehkand and A. Jodayree Akbarfam. 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. E. Montrol, “Quantum theory on a network,” Journal of Mathematical Physics, vol. 11, pp. 635–648, 1970. View at Google Scholar
  2. M. D. Faddeev and B. S. Pavlov, “A model of free electrons and the scattering problem,” Akademiya Nauk SSSR, vol. 55, no. 2, pp. 257–268, 1983. View at Google Scholar
  3. K. Ruedenberg and C. W. Scherr, “Free-electron network model for conjugated systems—I. Theory,” Journal of Chemical Physics, vol. 21, pp. 1565–1581, 1953. View at Google Scholar
  4. V. Kostrykin and R. Schrader, “Kirchhoff's rule for quantum wires,” Journal of Physics A, vol. 32, no. 4, pp. 595–630, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Kuchment, “Differential and pseudo-differential operators on graphs as models of mesoscopic systems,” in Proceedings of the Analysis and Applications (ISAAC '01), vol. 10, pp. 7–30, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003.
  6. P. Kuchment, “Graph models for waves in thin structures,” Waves in Random Media, vol. 12, no. 4, pp. R1–R24, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. G. Berkolaiko, E. B. Bogomolny, and J. P. Keating, “Star graphs and Šeba billiards,” Journal of Physics A, vol. 34, no. 3, pp. 335–350, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Currie, Spectral theory of differential operators on graphs, Ph.D. thesis, University of the Witwatersrand, Johannesburg, South Africa, 2006.
  9. Y. V. Pokornyi and A. V. Borovskikh, “Differential equations on networks (geometric graphs),” Journal of Mathematical Sciences, vol. 119, no. 6, pp. 691–718, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Y. V. Pokornyi and V. L. Pryadiev, “The qualitative Sturm-Liouville theory on spatial networks,” Journal of Mathematical Sciences, vol. 119, no. 6, pp. 788–835, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. V. Adamyan, “Scattering matrices for microschemes,” in Operator Theory and Complex Analysis, vol. 59, pp. 1–10, Birkhäuser, Basel, Switzerland, 1992. View at Google Scholar · View at Zentralblatt MATH
  12. R. Carlson, “Hill's equation for a homogeneous tree,” Electronic Journal of Differential Equations, vol. 23, pp. 1–30, 1997. View at Google Scholar · View at Zentralblatt MATH
  13. N. I. Gerasimenko and B. S. Pavlov, “A scattering problem on noncompact graphs,” Akademiya Nauk SSSR, vol. 74, no. 3, pp. 345–359, 1988. View at Publisher · View at Google Scholar
  14. Y. B. Melnikov and B. S. Pavlov, “Two-body scattering on a graph and application to simple nanoelectronic devices,” Journal of Mathematical Physics, vol. 36, no. 6, pp. 2813–2825, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. Melnikov and B. Pavlov, “Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators,” Journal of Mathematical Physics, vol. 42, no. 3, pp. 1202–1228, 2001. View at Publisher · View at Google Scholar
  16. V. Pivovarchik, “Inverse problem for the Sturm-Liouville equation on a simple graph,” SIAM Journal on Mathematical Analysis, vol. 32, no. 4, pp. 801–819, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. V. Pivovarchik, “Inverse problem for the Sturm-Liouville equation on a star-shaped graph,” Mathematische Nachrichten, vol. 280, no. 13-14, pp. 1595–1619, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. C. F. Yang, “Inverse spectral problems for the Sturm-Liouville operator on a d-star garph,” Journal of Mathematical Analysis and Applications, vol. 365, no. 2, pp. 742–749, 2010. View at Google Scholar
  19. G. Freiling and V. Yurko, Inverse Sturm-Liouville Problems and Their Applications, Nova Science, Huntington, NY, USA, 2001.
  20. V. A. Marchenko, Sturm-Liouville Operators and Applications, vol. 22, Birkhäuser, Basel, Switzerland, 1986.
  21. V. Pivovarchik, “Direct and inverse three-point Sturm-Liouville problem with parameter-dependent boundary conditions,” Asymptotic Analysis, vol. 26, no. 3-4, pp. 219–238, 2001. View at Google Scholar · View at Zentralblatt MATH
  22. B. Y. Levin, Lectures on Entire Functions, vol. 150, American Mathematical Society, Providence, RI, USA, 1996.
  23. R. P. Boas,, Entire Functions, Academic Press, New York, NY, USA, 1954.
  24. V. Pivovarchik and H. Woracek, “Sums of Nevanlinna functions and differential equations on star-shaped graphs,” Operators and Matrices, vol. 3, no. 4, pp. 451–501, 2009. View at Google Scholar · View at Zentralblatt MATH
  25. B. Ja. Levin and Ĭ. V. Ostrovskii, “Small perturbations of the set of roots of sine-type functions,” Izvestiya Akademii Nauk SSSR, vol. 43, no. 1, pp. 87–110, 1979 (Russian), English translatin in Mathematics of the USSR-Izvestiya, vol. 14, no. 1, pp. 79–101, 1980. View at Google Scholar
  26. N. Naimark, Linear Differential Operators, Parts I and II, Frederick Ungar, New York, NY, USA, 1968.
  27. V. N. Pivovarchik, “An inverse Sturm-Liouville problem by three spectra,” Integral Equations and Operator Theory, vol. 34, no. 2, pp. 234–243, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. B. J. Levin and J. I. Ljubarskiĭ, “Interpolation by entire functions belonging to special classes and related expansions in series of exponentials,” Izvestiya Akademii Nauk SSSR, vol. 39, no. 3, pp. 657–702, 1975. View at Google Scholar
  29. F. Gesztesy and B. Simon, “On the determination of a potential from three spectra,” in Differential Operators and Spectral Theory, vol. 189, pp. 85–92, American Mathematical Society, Providence, RI, USA, 1999. View at Google Scholar · View at Zentralblatt MATH