Spectral Problems for Operator Pencils in Non-Separated Root Zones

Variational principles for real eigenvalues of self-adjoint operator pencils in non-separated root zones are studied.

Spectral Problems for Operator Pencils in Non-Separated Root Zones

Variational principles for real eigenvalues of self-adjoint operator pencils in non-separated root zones are studied.

___

  • Abramov, Yu.S.: Variational Methods in the theory of operator pencils. Izd. Leningradsk. Univer. 1983.
  • Abramov, Yu.S.: Pencils of waveguide type and related extremal problems. J. Soviet Math. , 6, 1278- 288 (1993).
  • Barston, E.M.: A minimax principles for nonoverdamped systems. Int. J. Eng. Sci. 12, 413- (1974).
  • Binding , P., Eschwe, D., Langer, H.: Variational principles for real eigenvalues of self- adjoint operator pencils. Integral Equations and Operator Theory. 38, 2. 190- 206 (2000).
  • Eschwe, D., Langer, H.: Triple variational principles for eigenvalues of self-adjoint operators and operator functions. SIAM J. Math. Anal. 34, 1, 228-238 (2002).
  • Eschwe, D., Langer, M.: Variational principles for eigenvalues of self-adjoint operator functions. Integral Equations and Operator Theory. 49, 287- 321 (2004).
  • Griniv, R. O., Mel’nik, T.A.: On the singular Rayleigh Functional. Mathematical Notes. vol.60, 1, 97- 100 (1996).
  • Hasanov, M.: On the spectrum of a weak class of operator pencils of waveguide type. Math. Nachr. 279, 8, 843-853 (2006).
  • Hasanov, M.: An approximation method in the variational theory of the spectrum of operator pencils. Acta Appl. Math. Vol. 71, 2, 117- 126 (2002).
  • Markus, A.S.: Introduction to spectral theory of polynomial operator pencils. AMS. Prov- idence. 1988.
  • Voss, H.: A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid- solid vibration. Applications of Mathematics. 48, 6, 607– (2003).
  • Voss, H., Werner, B.: A minimax principle for nonlinear eigenvalue problems with applica- tions to nonoverdamped systems. Math. Methods Appl. Sci. 4 , 415–424 (1982).
  • Zilbergleit, A., Kopilevich, Yu.: Spectral theory of guided waves. Institute of Physics Publishing. Bristol, 1996. M. HASANOV
  • Istanbul Technical University, Department of Mathematics Maslak, 34469, ˙Istanbul-TURKEY e-mail: hasanov@itu.edu.tr