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An Approximation Method in the Variational Theory of the Spectrum of Operator Pencils

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Abstract

An approximation method, based on a theorem on approximating general operator-valued functions by piecewise-linear ones, is presented and analyzed. Using this method, variational characteristics of the spectrum of a class of operator functions are established.

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References

  1. Abramov, Ju. S.: Variational Methods in the Theory of Operator Pencils, Izd. Leningradsk. Univ., 1983 (Russian).

  2. Binding, P. A. and Ye, Q.: Variational principles without definiteness conditions, SIAM J. Math. Anal. 22(6) (1991), 1575–1583.

    Google Scholar 

  3. Hasanov (Gasanov), M.: Approximation and variational characteristics of the spectrum of nonsmooth Rayleigh systems, J. Math. Sci. 72(6) (1994), 3385–3394.

    Google Scholar 

  4. Hasanov (Gasanov), M. and Cesur, Y.: On a nonlinear eigenvalue problem, Integral Equations Operator Theory 29 (1997), 491–500.

    Google Scholar 

  5. Maksudov, F. G. and Hasanov (Gasanov, M. G.), M.: On the variational theory of the spectrum of operator pencils, Dokl. Akad. Nauk 325(5) (1992), 915–918 English translation in Russian Acad. Sci. Dokl. Math. 46(1) (1993), 126–130.

    Google Scholar 

  6. Markus, A. S.: Introduction to the Spectral Theory of Polynomial Operator Pencils, Amer. Math. Soc., Providence, RI, 1988.

    Google Scholar 

  7. Najman, B. and Ye, Q.: A minimax characterization for eigenvalues of Hermitian pencils, I, II, Linear Algebra Appl. 144 (1991), 217–230; 191 (1997), 183–197.

    Google Scholar 

  8. Nirenberg, L. and Treves, F.: On local solvability of linear partial differential equations-I, II, Comm. Pure Appl. Math. 23 (1970), 1–38 and 23 (1970), 459–510.

    Google Scholar 

  9. Rogers, E. H.: Variational properties of nonlinear spectra, J. Math. Mech. 18(6) (1968), 479–490.

    Google Scholar 

  10. Stenger, W.: An inequality for eigenvalues of self-adjoint operators, Bull. Amer. Math. Soc. 73 (1967), 487–489.

    Google Scholar 

  11. Turner, R.: Some variational principles for a nonlinear eigenvalue problem, J. Math. Anal. Appl. 17 (1967), 151–165.

    Google Scholar 

  12. Turner, R.: A class of nonlinear eigenvalue problems, J. Funct. Anal. 2 (1968), 297–322.

    Google Scholar 

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Hasanov, M. An Approximation Method in the Variational Theory of the Spectrum of Operator Pencils. Acta Applicandae Mathematicae 71, 117–126 (2002). https://doi.org/10.1023/A:1014545418177

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