Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Abstract and Applied Analysis, enter your email address in the box below.

Abstract and Applied Analysis
Volume 2009, Article ID 934905, 21 pages
http://dx.doi.org/10.1155/2009/934905
Research Article

On the Differential Operators with Periodic Matrix Coefficients

O. A. Veliev

Department of Mathematics, Dogus University, Acıbadem, Kadiköy, Istanbul, Turkey

Received 26 March 2009; Revised 22 July 2009; Accepted 26 September 2009

Academic Editor: Ağacik Zafer

Copyright © 2009 O. A. Veliev. 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. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburg, UK, 1973.
  2. I. M. Gelfand, “Expansion in characteristic functions of an equation with periodic coefficients,” Soviet Mathematics—Doklady, vol. 73, pp. 1117–1120, 1950. View at Google Scholar · View at MathSciNet
  3. F. G. Maksudov and O. A. Veliev, “Spectral analysis of differential operators with periodic matrix coefficients,” Differential Equations, vol. 25, no. 3, pp. 271–277, 1989. View at Google Scholar
  4. D. C. McGarvey, “Operators commuting with translation by one. II. Differential operators with periodic coefficients in Lp(−∞,∞),” Journal of Mathematical Analysis and Applications, vol. 11, pp. 564–596, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. D. Birkhoff, “Boundary value and expansion problems of ordinary linear differential equations,” Transactions of the American Mathematical Society, vol. 9, no. 4, pp. 373–395, 1908. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. D. Tamarkin, Some General Problems of the Theory of Ordinary Linear Differential Equations, Petrograd, 1917.
  7. M. A. Naimark, Linear Differential Operators, George G. Harap, London, UK, 1967.
  8. V. A. Marchenko, Sturm-Liouville Operators and Applications, vol. 22 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1986. View at MathSciNet
  9. N. Dunford and J. T. Schwartz, Linear Operators, Part 3, Spectral Operators, Wiley Classics Library, John Wiley & Sons, New York, NY, USA, 1988. View at MathSciNet
  10. V. A. Yakubovich and V. M. Starzhinski, Linear Differential Equations with Periodic Coefficients, John Wiley & Sons, New York, NY, USA, 1975.
  11. O. A. Veliev, “On the spectrum of the Schrödinger operator with periodic potential,” Soviet Mathematics—Doklady, vol. 27, no. 1, pp. 234–237, 1983. View at Google Scholar
  12. O. A. Veliev, “On Hill's operator with a matrix potential,” Mathematische Nachrichten, vol. 281, no. 9, pp. 1341–1350, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. Chelkak and E. Korotyaev, “Spectral estimates for Schrödinger operators with periodic matrix potentials on the real line,” International Mathematics Research Notices, vol. 2006, Article ID 60314, 41 pages, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet