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Exponential behaviour of eigenfunctions and gaps in the essential spectrum

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References

  1. F. V. Atkinson, Limit-n criteria of integral type, Proc.Royal Soc. Edinb.(A), 73(1975), 167–198.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. I. Brinck, Self-adjointness and spectra of Sturm-Liouville operators, Math. Scand. 7(1959), 219–239.

    MathSciNet  MATH  Google Scholar 

  3. N. Dunford and J. T. Schwartz, Linear Operators. Part II, (Interscience, New York, 1963).

    MATH  Google Scholar 

  4. M. S. P. Eastham, Gaps in the essential spectrum associated with singular differential operators, Quart. Jour. Math. (Oxford) (2), 18(1967), 155–168.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M. S. P. Eastham, Asymptotic estimates for the lengths of the gaps in the essential spectrum of self-adjoint differential operators, Proc. Yoral Soc. Edinb.(A), 74(1976), 239–252.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M. S. P. Eastham, Gaps in the essential spectrum of even-order self-adjoint differential operators, Proc. London Math. Soc.(3), 34(1977), 213–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W. N. Everitt, On the spectrum of a second-order linear differential equation with a p-integrable coefficient, Applicable Analysis, 2(1972), 143–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, (Israel Program for Scientific Translations, Jerusalem, 1965).

    Google Scholar 

  9. S. G. Halvorsen, Counterexamples in the spectral theory of singular Sturm-Liouville operators, Mathematics no. 9/74, Matematisk Institutt, Universitet i Trondheim, Trondheim, Norway.

    Google Scholar 

  10. P. Hartman and C. R. Putnam, The gaps in the essential spectra of gave equations, Amer. Jour. Math. 72(1950), 849–862.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. R. M. Kauffman, On the growth of solutions in the oscillatory case, Proc. Amer. Math. Soc. 51(1975), 49–54

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. M. Kauffman, Gaps in the essential spectrum for second order systems, Proc. Amer. Math. Soc. 51(1975), 55–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. A. C. Lazer, A stability condition for the differential equation y″+p(x)y=0, Michigan Math. Jour. 12(1965), 193–196.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. C. R. Putnam, On isolated eigenfunctions associated with bounded potentials, Amer. Jour. Math. 82(1950), 135–147.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. D. A. R. Rigler, On a strong limit-point condition and an integral inequality associated with a symmetric matrix differential expression, Proc. Royal Soc. Edinb. (A), 76(1976), 155–159.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. L. B. Zelenko, Spectrum of Schrödinger's equation with a complex pseudoperiodic potential, Parts I and II, Diff. Urav. 12(1976), 806–814 and 1417–1426.

    Google Scholar 

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© 1980 Springer-Verlag

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Atkinson, F.V. (1980). Exponential behaviour of eigenfunctions and gaps in the essential spectrum. In: Everitt, W.N. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091372

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  • DOI: https://doi.org/10.1007/BFb0091372

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  • Print ISBN: 978-3-540-10252-6

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