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Deficiency indices and properties of spectrum of some classes of differential operators

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Part of the Lecture Notes in Mathematics book series (LNM,volume 448)

Keywords

  • Differential Operator
  • Elliptic Operator
  • Elliptic System
  • Operator Coefficient
  • Deficiency Index

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References

  1. V. I. Kogan and F. S. Rofe-Beketov, On square-integrable solutions of symmetric systems of differential equations of arbitrary order (to appear in the Proc. Roy. Soc. Edinb.).

    Google Scholar 

  2. V. I. Kogan and F. S. Rofe-Beketov, On the question of the deficiency indices of differential operators with complex coefficients, Matem. Fizika i funktsional Anal., vyp.2 (Kharkov, 1971), 45–60 (Engl. Transl. to appear in the Proc. Roy. Soc. Edinb.).

    Google Scholar 

  3. F. S. Rofe-Beketov, Self-adjoint extensions of differential operators in a space of vector functions, DAN SSSR, 184, No. 5 (1969), 1034–1037.

    MathSciNet  MATH  Google Scholar 

  4. W. N. Everitt, Integrable-square, analytic solutions of odd-order, formally symmetric, ordinary differential equations, Proc. Lond. Math. Soc., (3), 25 (1972), 156–182.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. F. V. Atkinson, Discrete and continuous boundary problems, Acad. Press, N.Y., 1964.

    MATH  Google Scholar 

  6. G. A. Kalyabin, The number of solutions in L2(0, ∞) of a self-adjoint system of second order differential equations, Funktsional Anal. i Prilozhen., 6 No. 3 (1972), 74–76.

    Google Scholar 

  7. J. C. Gokhberg and M. G. Krein, Theory of Volterra operators in Hilbert space and its applications, "Nauka", Moscow, 1967.

    MATH  Google Scholar 

  8. B. M. Levitan and I. S. Sargsyan, Introduction to spectral theory, "Nauka", Moscow, 1970.

    MATH  Google Scholar 

  9. M. A. Naimark, Linear differential operators, 2nd edn, "Nauka", Moscow, 1969.

    MATH  Google Scholar 

  10. W. Wasow, Asymptotic expansions for ordinary differential equations, John Wiley and Sons, N.Y., 1965.

    MATH  Google Scholar 

  11. A. G. Brusentsev and F. S. Rofe-Beketov, On the self-adjointness of high-order elliptic operators, Funktsional Anal. i Prilozhen., 7 No. 4 (1973), 78–79.

    MATH  Google Scholar 

  12. A. G. Brusentsev and F. S. Rofe-Beketov, Conditions for the self-adjointness strongly elliptic systems of arbitrary-order, (to appear in Matem. Sbornik).

    Google Scholar 

  13. A. G. Brusentsev, Certain problems of the qualitative spectral analysis of arbitrary-order elliptic systems, Matem. Fizika i Funktsional. Anal., vyp.4 (Kharkov, 1973), 93–116.

    Google Scholar 

  14. F. S. Rofe-Beketov and A. M. Holkin, Conditions for the self-adjointness of second-order elliptic operators of the general type, Theor. Funktsiy Funktsional. Anal. i Prilozh., vyp. 17 (1973), 41–51.

    MathSciNet  Google Scholar 

  15. E. C. Titchmarsh, Eigenfunctions expansions associated with second-order differential equations, Part II, Oxford, at the Claredon Press, 1958.

    MATH  Google Scholar 

  16. F. S. Rofe-Beketov, Conditions for the self-adjointness of the Schrödinger operator, Mat. Zametki, 8, No. 6 (1970), 741–751.

    MathSciNet  Google Scholar 

  17. I. M. Glazman, Direct methods of qualitative spectral analysis, "Fizmatgiz", Moscow, 1963. Eng. transl.

    MATH  Google Scholar 

  18. I. M. Gelfand and G. E. Shilov, Certain questions of differential equations theory, "Fizmatgiz", Moscow, 1958.

    Google Scholar 

  19. Ju. M. Berezanskiy, Expansions in eigenfunctions of self-adjoint operators, Am. Math. Soc., Monograph. Transl., vol. 17, 1968.

    Google Scholar 

  20. F. S. Rofe-Beketov, A test for the finiteness of the number of discrete levels introduced into the gaps of a continuous spectrum by perturbations of a periodic potential, DAN SSSR, 156, No. 3 (1964), 515–518.

    MathSciNet  MATH  Google Scholar 

  21. F. S. Rofe-Beketov, Hill’s operator perturbation, which has a first moment and a non-vanishing integral, introduces one discrete level into each distant spectral gap, Matem. Fizika i Funktsional. Anal., vyp. 4, (Kharkov, 1973), 158–159.

    MathSciNet  Google Scholar 

  22. V. I. Khrabustovskiy, On perturbations of the spectrum of self-adjoint differential operators with periodic matrix coefficients, ibid., vyp. 4, (Kharkov, 1973), 117–138.

    Google Scholar 

  23. V. I. Khrabustovskiy, On perturbations of the spectrum of arbitrary order self-adjoint differential operators with periodic matrix coefficients, ibid, vyp.5 (to appear).

    Google Scholar 

  24. F. S. Rofe-Beketov, On the spectrum of non-self-adjoint differential operators with periodic coefficients, DAN SSSR, 152, No. 6 (1963), 1312–1315.

    MathSciNet  MATH  Google Scholar 

  25. F. S. Rofe-Beketov and V. I. Khrabustovskiy, The stability of the solutions of Hill’s equation with an operator coefficient, Teor. Funktsiy Funktsional. Anal. i Prilozh., vyp. 13 (1971), 140–147.

    Google Scholar 

  26. F. S. Rofe-Beketov and V. I. Khrabustovskiy, The stability of the solutions of Hill’s equation with an operator coefficient that has a non-negative mean value, ibid, vyp. 14 (1971), 101–105.

    Google Scholar 

  27. F. S. Rofe-Beketov and V. I. Khrabustovskiy, Letters to the editors, ibid, vyp. 14 (1971), 195.

    Google Scholar 

  28. E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, N.Y. and London, 1955.

    MATH  Google Scholar 

  29. V. A. Želudev, The perturbation of the spectrum of the one-dimensional selfadjoint Schrödinger operator with periodic potential, Problemy Matem. Fiziki, No. 4 (Leningrad, 1970), 61–82.

    Google Scholar 

  30. Ju. L. Daleckii and M. G. Krein, Stability of the solutions of differential equations in Banach space, "Nauka", Moscow, 1970.

    Google Scholar 

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© 1975 Springer-Verlag

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Rofe-Beketov, F.S. (1975). Deficiency indices and properties of spectrum of some classes of differential operators. In: Everitt, W.N. (eds) Spectral Theory and Differential Equations. Lecture Notes in Mathematics, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067091

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  • DOI: https://doi.org/10.1007/BFb0067091

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07150-1

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