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Property of the eigenvectors of quadratic operator pencils of being a basis

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Literature cited

  1. G. V. Radzievskii, “A quadratic pencil of operators,” Preprint Mat. Inst. Akad. Nauk Ukr. SSR, Kiev (1976).

  2. A. I. Virozub, “On the energy completeness of the system of elementary solutions of a differential equation in a Hilbert space,” Funkts. Anal. Prilozhen.,9, No. 1, 52–53 (1975).

    Google Scholar 

  3. M. B. Orazov and A. A. Shkalikov, “On the property of being an n-multiple basis of the eigenfunctions of certain regular boundary-value problems,” Sib. Mat. Zh.,17, No. 3, 627–639 (1976).

    Google Scholar 

  4. M. G. Krein and G. K. Langer, “On certain mathematical principles of the linear theory of damped vibrations of continuums,” in: Proceedings of the International Symposium on the Application of the Theory of Functions in the Mechanics of Continuous Media [in Russian], Vol. 2, Nauka, Moscow (1965), pp. 283–322.

    Google Scholar 

  5. A. G. Kostyuchenko and M. B. Orazov, “Certain properties of the roots of a self-adjoint quadratic pencil,” Funks. Anal. Prilozhen.,9, No. 4, 28–40 (1975).

    Google Scholar 

  6. M. B. Orazov, “Completeness of the eigen- and associated vectors of a self-adjoint quadratic pencil,” Funkts. Anal. Prilozhen.,10, No. 2, 82–83 (1976).

    Google Scholar 

  7. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Nonselfadjoint Linear Operators, Amer. Math. Soc. (1969).

  8. M. B. Orazov, “On the St. Venant principle for the equations of stationary vibrations of an elastic half-cylinder,” in: Abstracts of the Reports of the Republican Symposium on Differential Equations [in Russian], Ashkhabad (1978).

  9. J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag (1972).

  10. Ya. D. Tamarkin, Some General Problems of the Theory of Ordinary Differential Equations [in Russian], Petrograd (1917).

  11. M. A. Naimark, Linear Differential Operators, Ungar.

  12. A. M. Minkin, “The regularity of self-adjoint boundary conditions,” Mat. Zametki,22, No. 6, 835–846 (1977).

    Google Scholar 

  13. I. D. Evzerov, “Domains of the fractional powers of ordinary differential operators in the spaces Lp,” Mat. Zametki,21, No. 4, 509–518 (1977).

    Google Scholar 

  14. A. A. Shkalikov, “Weakly perturbed pencils of operators,” in: Abstracts of the Reports of the Republican Symposium on Differential Equations [in Russian], Ashkhabad (1978).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. A. Shkalikov

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  1. A. A. Shkalikov
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Translated from Matematicheskie Zametki, Vol. 30, No. 3, pp. 371–385, September, 1981.

In conclusion, the author thanks A. G. Kostyuchenko and G. V. Radzievskii for discussions regarding the present note.

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Shkalikov, A.A. Property of the eigenvectors of quadratic operator pencils of being a basis. Mathematical Notes of the Academy of Sciences of the USSR 30, 676–684 (1981). https://doi.org/10.1007/BF01141624

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