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Journal of Function Spaces and Applications
Volume 2012, Article ID 789875, 13 pages
Research Article

G-Convergence of Dirac Operators

Department of Mathematical Sciences, University of Gothenburg, 412 96 Gothenburg, Sweden

Received 2 November 2011; Revised 12 March 2012; Accepted 16 March 2012

Academic Editor: Bjorn Birnir

Copyright © 2012 Hasan Almanasreh and Nils Svanstedt. 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. De Giorgi and S. Spagnolo, “Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine,” Bollettino della Unione Matematica Italiana, vol. 8, pp. 391–411, 1973. View at Google Scholar · View at Zentralblatt MATH
  2. S. Spagnolo, “Sul limite delle soluzioni di problemi di cauchy relativi all'equazione del calore,” Annali della Scuola Normale Superiore di Pisa, vol. 21, pp. 657–699, 1967. View at Google Scholar · View at Zentralblatt MATH
  3. S. Spagnolo, “Convergence in energy for elliptic operators,” in Proceedings of the 3rd Symposium on the Numerical Solution of Partial Differential Equations, pp. 469–498, Academic Press, College Park, Md, USA, 1976.
  4. F. Murat, “H-convergence,” in Séminaire d'Analyse Fonctionelle et Numérique de I'Université d'Alger, 1977.
  5. L. Tartar, Cours Peccot au Collège de France, Paris, France, 1977.
  6. L. Tartar, “Quelques remarques sur I'homogénéisation,” in Proceedings of the Japan-France Seminar on Functional Analysis and Numerical Analysis, pp. 469–482, Japan Society for the Promotion of Science, 1978.
  7. G. Dal Maso, An Introduction to Γ-Convergence, Birkhäuser, Boston, Mass, USA, 1993. View at Zentralblatt MATH
  8. B. Thaller, The Dirac Equation, Springer, Berlin, Germany, 1993.
  9. J. Weidmann, Linear Operators in Hilbert Spaces, Springer, New York, NY, USA, 1980.
  10. J. Weidmann, Lineare Operatoren in Hilberträumen, Teubner, Wiesbaden, Germany, 2003.
  11. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, Germany, 1976.
  12. A. Defranceschi, “An introduction to Homogenization and G-convergence,” in Proceedings of the International Conference on Technology of Plasticity (ICTP '93), School on Homogenization Lecture Notes, Trieste, Italy, 1993.
  13. N. Svanstedt, “G-convergence of parabolic operators,” Nonlinear Analysis: Theory, Methods & Applications, vol. 36, no. 7, pp. 807–843, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. S. Birman and M. Z. Solomjak, Spectral Theory of Selfadjoint Operators in Hilbert Space, North-Holland, Dordrecht, The Netherlands, 1987.
  15. J. Weidmann, “Strong operator convergence and spectral theory of ordinary differential operators,” Universitatis Iagellonicae. Acta Mathematica, no. 34, pp. 153–163, 1997. View at Google Scholar · View at Zentralblatt MATH
  16. O. A. Oleinik, A. S. Shamaev, and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization, Elsevier Science, Amsterdam, The Netherlands, 1992.
  17. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, The Netherlands, 1978.