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Variational characterizations for eigenfunctions of analytic self-adjoint operator functions

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Języki publikacji
EN
Abstrakty
EN
In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.
Rocznik
Strony
307--321
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
  • National Technical University of Athens Dept. of Mathematics Zografou Campus Athens 15780, Greece
autor
  • National Technical University of Athens Dept. of Mathematics Zografou Campus Athens 15780, Greece
Bibliografia
  • [1] R. Bhatia, Matrix Analysis, Springer-Verlag, New York 1997.
  • [2] P. Binding, D. Eschwe, H. Langer, Variational principles for real eigenvalues of self-adjoint operator pencils, Integral Equations Operator Theory 38 (2000), 190-206.
  • [3] D. Eschwe, M. Langer, Variational principles for eigenvalues of self-adjoint operator functions, Integral Equations Operator Theory 49 (2004), 287-321.
  • [4] S. Frieland, A generalization of the Motzkin-Taussky theorem, Linear Algebra Appl. 36 (1981), 103-109.
  • [5] I. Gohberg, P. Lancaster, L. Rodman, Matrix Polynomials, Academic Press, New York 1982.
  • [6] R.O. Hryniv, P. Lancaster, On the perturbation of analytic matrix functions, Integral Equations Operator Theory 34 (1999), 325-338.
  • [7] Y. Ikebe, T. Inagaki, S. Miyamoto, The monotonicity theorem, Cauchy's interlace theorem, and the Gourant-Fischer theorem, Amer. Math. Monthly 94 (1987), 352-354.
  • [8] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1995.
  • [9] P. Lancaster, J. Maroulas, P. Zizler, The numerical range of selfadjoint matrix polynomials, Oper. Theory: Adv. Appl. 106 (1998) 291-304.
  • [10] P. Lax, Linear Algebra, J. Wiley and Sons Inc., N.Y., 1997.
  • [11] A.S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils, vol. 71, Translations of Math. Monographs, American Math. Soc, Providence, 1988.
  • [12] J. Maroulas, P. Psarrakos, M. Tsatsomeros, Separable characteristic polynomials of pencils and property V, Electron. J. of Linear Algebra 7 (2000), 182-190.
  • [13] N. Moiseyev, S. Frieland, The association of resonant states with incomplete spectrum of finite complex scaled Hamiltonian matrices, Phys. Rev. 22 (1980), 619-624.
  • [14] T.S. Motzkin, O. Taussky, Pairs of matrices with property L, Trans. Amer. Math. Soc. 73 (1952), 108-114.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-daef3834-1557-45f7-a641-faa04cc60d3c
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