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Point Spectrum of Singularly Perturbed Self-Adjoint Operators

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We study the inverse spectral problem for the point spectrum of singularly perturbed self-adjoint operators.

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REFERENCES

  1. M. G. Krein, “Theory of self-adjoint extensions of semibounded Hermite operators and its applications. I,” Mat. Sb., 20(62), No. 3, 431–495 (1947).

    MATH  MathSciNet  Google Scholar 

  2. V. A. Derkach and M. M. Malamud, “General resolvents and the boundary-value problem for Hermitian operators with gaps,” J. Funct. Anal., 95, 1–95 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Albeverio, J. F. Brasche, and H. Neidhardt, “On inverse spectral theory of self-adjoint extensions: mixed types of spectra,” J. Funct. Anal., 154, 130–173 (1998).

    MathSciNet  MATH  Google Scholar 

  4. J. F. Brasche, M. M. Malamud, and H. Neidhardt, “Weyl function and spectral properties of self-adjoint extensions,” Integr. Equat. Oper. Theor., 43, 264–289 (2002).

    MathSciNet  MATH  Google Scholar 

  5. S. Albeverio, J. F. Brasche, M. M. Malamud, and H. Neidhardt, Inverse Spectral Theory for Symmetric Operators with Several Gaps: Scalar-Type Weyl Functions, Preprint No. 166, Bonn (2004).

  6. S. Albeverio and L. Nizhnik, “On the number of negative eigenvalues of one-dimensional Schrodinger operators with point interaction,” Lett. Math. Phys., 65, 27–35 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. E. Dudkin and V. D. Koshmanenko, “On the point spectrum of self-adjoint operators that appears under singular perturbations of finite rank,” Ukr. Mat. Zh., 55, No.9, 1269–1276 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. Koshmanenko, “A variant of inverse negative eigenvalue problem in singular perturbation theory,” Meth. Funct. Anal. Top., 8, No.1, 49–69 (2002).

    MATH  MathSciNet  Google Scholar 

  9. S. Albeverio, M. Dudkin, A. Konstantinov, and V. Koshmanenko, On the Point Spectrum of \(H_{ - 2}\) Singular Perturbations, Preprint No. 122, Bonn (2003).

  10. S. Albeverio, A. Konstantinov, and V. Koshmanenko, On Inverse Spectral Theory for Singularly Perturbed Operators: Point Spectrum, Preprint No. 182, Bonn (2004).

  11. Yu. M. Berezans'kyi, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  12. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1966).

    MATH  Google Scholar 

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 654–658, May, 2005.

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Konstantinov, O.Y. Point Spectrum of Singularly Perturbed Self-Adjoint Operators. Ukr Math J 57, 776–781 (2005). https://doi.org/10.1007/s11253-005-0227-2

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  • DOI: https://doi.org/10.1007/s11253-005-0227-2

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