Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 358912, 12 pages
http://dx.doi.org/10.1155/2011/358912
Research Article

Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

Department of Mathematics, Karamanoğlu Mehmetbey University, 70100 Karaman, Turkey

Received 8 March 2011; Accepted 5 April 2011

Academic Editor: Narcisa C. Apreutesei

Copyright © 2011 Nihal Yokuş. 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. M. A. Naĭmark, “Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis,” American Mathematical Society Translations, vol. 16, pp. 103–193, 1960. View at Google Scholar
  2. V. E. Lyance, “A differential operator with spectral singularities I,” American Mathematical Society Transactions Series 2, vol. 60, pp. 185–225, 1967. View at Google Scholar
  3. V. E. Lyance, “A differential operator with spectral singularities II,” American Mathematical Society Transactions Series 2, vol. 60, pp. 227–283, 1967. View at Google Scholar
  4. A. M. Krall, “The adjoint of a differential operator with integral boundary conditions,” Proceedings of the American Mathematical Society, vol. 16, pp. 738–742, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. A. M. Krall, “A nonhomogeneous eigenfunction expansion,” Transactions of the American Mathematical Society, vol. 117, pp. 352–361, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. M. Krall, “Second order ordinary differential operators with general boundary conditions,” Duke Mathematical Journal, vol. 32, pp. 617–625, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. M. Krall, “Nonhomogeneous differential operators,” The Michigan Mathematical Journal, vol. 12, pp. 247–255, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. M. Krall, “On non-self-adjoint ordinary differential operators of the second order,” Doklady Akademii Nauk SSSR, vol. 165, pp. 1235–1237, 1965. View at Google Scholar
  9. M. G. Gasymov, “Expansion in terms of the solutions of a scattering theory problem for the non-selfadjoint Schrödinger equation,” Soviet Mathematics—Doklady, vol. 9, pp. 390–393, 1968. View at Google Scholar
  10. M. G. Gasymov and F. G. Maksudov, “The principal part of the resolvent of nonselfadjoint operators in the neighborhood of spectral singularities,” Functional Analysis and Its Applications, vol. 6, no. 3, pp. 185–192, 1972. View at Google Scholar
  11. M. Adıvar and E. Bairamov, “Spectral properties of non-selfadjoint difference operators,” Journal of Mathematical Analysis and Applications, vol. 261, no. 2, pp. 461–478, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Adıvar and E. Bairamov, “Difference equations of second order with spectral singularities,” Journal of Mathematical Analysis and Applications, vol. 277, no. 2, pp. 714–721, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Bairamov, Ö. Çakar, and A. M. Krall, “An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities,” Journal of Differential Equations, vol. 151, no. 2, pp. 268–289, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. Bairamov, Ö. Çakar, and A. M. Krall, “Non-selfadjoint difference operators and Jacobi matrices with spectral singularities,” Mathematische Nachrichten, vol. 229, pp. 5–14, 2001. View at Google Scholar · View at Zentralblatt MATH
  15. E. Bairamov, Ö. Çakar, and A. M. Krall, “Spectral properties, including spectral singularities, of a quadratic pencil of Schrödinger operators on the whole real axis,” Quaestiones Mathematicae, vol. 26, no. 1, pp. 15–30, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. E. Bairamov, Ö. Cakar, and C. Yanik, “Spectral singularities of the Klein-Gordon s-wave equation,” Indian Journal of Pure and Applied Mathematics, vol. 32, no. 6, pp. 851–857, 2001. View at Google Scholar
  17. E. Bairamov and A. O. Çelebi, “Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators,” The Quarterly Journal of Mathematics. Oxford. Second Series, vol. 50, no. 200, pp. 371–384, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. E. Bairamov and Ö. Karaman, “Spectral singularities of Klein-Gordon s-wave equations with an integral boundary condition,” Acta Mathematica Hungarica, vol. 97, no. 1-2, pp. 121–131, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. M. Krall, E. Bairamov, and Ö. Çakar, “Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition,” Journal of Differential Equations, vol. 151, no. 2, pp. 252–267, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A. M. Krall, E. Bairamov, and Ö. Çakar, “Spectral analysis of non-selfadjoint discrete Schrödinger operators with spectral singularities,” Mathematische Nachrichten, vol. 231, pp. 89–104, 2001. View at Google Scholar · View at Zentralblatt MATH
  21. V. A. Marchenko, “Expansion in eigenfunctions of non-selfadjoint singular second order differential operators,” American Mathematical Society Transactions Series 2, vol. 25, pp. 77–130, 1963. View at Google Scholar
  22. V. A. Marchenko, Sturm-Liouville Operators and Applications, vol. 22, Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1986.
  23. M. Jaulent and C. Jean, “The inverse s-wave scattering problem for a class of potentials depending on energy,” Communications in Mathematical Physics, vol. 28, pp. 177–220, 1972. View at Publisher · View at Google Scholar
  24. E. Bairamov and N. Yokus, “Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions,” Abstract and Applied Analysis, p. Art. ID 289596, 8, 2009. View at Google Scholar
  25. M. V. Keldysh, “On the completeness of the eigenfunctions of some classes of non-selfadjoint linear operators,” Soviet Mathematics—Doklady, vol. 77, no. 4, pp. 11–14, 1951. View at Google Scholar
  26. M. V. Keldysh, “On the completeness of the eigenfunctions of some classes of non-selfadjoint linear operators,” Russian Mathematical Surveys, vol. 26, no. 4, pp. 15–41, 1971. View at Google Scholar