On a boundary problem generated by a self-adjoint Sturm-Liouville differential operator on the entire real axis

  • M. M. Gekhtman
  • I. V. Stankevich


In Hilbert space L2(0, a), 0 < a < ∞, we consider the spectral problem generated by a Sturm-Liouville operator with real potential and boundary conditions which depend on the spectral parameter. The paper investigates the spectrum and the questions connected with the completeness of the system of eigenfunctions.


Boundary Condition Hilbert Space Differential Operator Real Axis Boundary Problem 
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Literature cited

  1. 1.
    T. Regge, “Construction of potentials from resonance parameters,” Nuovo Cimento,9, No. 3, 491–503 (1958).Google Scholar
  2. 2.
    T. Regge, “Analytical properties of the scattering matrix,” Nuovo Cimento,8, No. 5, 671–679 (1958).Google Scholar
  3. 3.
    A. O. Kravitskii, “On the expansion in eigenfunctions of one boundary problem,” Dokl. Akad. Nauk SSSR,170, No. 6, 1255–1258 (1966).Google Scholar
  4. 4.
    B. Ya. Levin, “Transformations of the Fourier and Laplace type by means of solutions of a secondorder differential equation,” Dokl. Akad. Nauk SSSR,106, No. 2, 187–190 (1956).Google Scholar
  5. 5.
    M. A. Naimark, Linear Differential Operators [in Russian], Moscow (1954).Google Scholar
  6. 6.
    J. Horn, Verwendung asymptotischer Darstellungen, Math. Ann.,49, No. 4, 473–496 (1897).Google Scholar
  7. 7.
    B. Ya. Levin, Distribution of the Roots of Integral Functions [in Russian], Moscow (1956).Google Scholar
  8. 8.
    M. A. Evgrafov, Asymptotic Bounds and Integral Functions [in Russian], Moscow (1962).Google Scholar

Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1970

Authors and Affiliations

  • M. M. Gekhtman
    • 1
    • 2
  • I. V. Stankevich
    • 1
    • 2
  1. 1.Dagestan State UniversityUSSR
  2. 2.Institute of Elementary Organic CompoundsAcademy of Sciences of the USSRUSSR

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