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Regular approximations of singular Sturm-Liouville problems

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Abstract

Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr{ of regular S-L problems with the properties

(i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr{

(ii) in the case when 5 is regular or limit-circle at each endpoint, a convergent sequence of eigenvalues from the individual members of {Sr{ has to converge to an eigenvalue of S

(iii) in the general case when S is bounded below, property (ii) holds for all eigenvalues below the essential spectrum of S.

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References

  1. Bailey, P. B., Everitt, W. N., and Zettl, A. “Computing eigenvalues of singular Sturm-Liouville problems”, Resultate für Mathematik v.20 (1991), 391–423.

    MathSciNet  MATH  Google Scholar 

  2. Kato, T., Perturbation theory for linear operators, second edition, Springer-Verlag, Heidelberg, 1980.

    MATH  Google Scholar 

  3. Krall, A. M. and Zettl, A. “Singular self-adjoint Sturm-Liouville problems”, Differential and Integral Equations, v. 1, no. 4 1988, 423–432.

    MathSciNet  MATH  Google Scholar 

  4. Naimark, M. A., Linear differential operators, vol. II, Ungar, New York, 1968.

    MATH  Google Scholar 

  5. Reed, M. and Simon, B. Methods of modern mathematical physics, vol. I, Academic Press, New York, 1972.

    MATH  Google Scholar 

  6. Weidmann, J., Linear operators in Hilbert spaces, Springer-Verlag, New York, 1980.

    Book  MATH  Google Scholar 

  7. Weidmann, J., Spectral theory of ordinary differential operators, Lecture Notes in Mathematics 1258, Springer-Verlag, Heidelberg, 1987.

    Google Scholar 

  8. Weidmann, J. and Stolz, G. “Approximation of isolated eigenvalues of ordinary differential operators”, (to appear).

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Authors and Affiliations

  1. 1008 Oro-Real N.E., Albuquerque, NM, 87123, USA

    P. B. Bailey

  2. Department of Mathematics, University of Birmingham, B15 2TT, England

    W. N. Everitt

  3. University of Frankfurt, W-6000, Frankfurt am Main 11, Germany

    J. Weidmann

  4. Dept. of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    A. Zettl

Authors
  1. P. B. Bailey
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  2. W. N. Everitt
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  3. J. Weidmann
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  4. A. Zettl
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Additional information

The work of these three authors was supported by NSF grant #DMS-9106470.

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Bailey, P.B., Everitt, W.N., Weidmann, J. et al. Regular approximations of singular Sturm-Liouville problems. Results. Math. 23, 3–22 (1993). https://doi.org/10.1007/BF03323127

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  • DOI: https://doi.org/10.1007/BF03323127

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