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A survey of spectral theory for pairs of ordinary differential operators

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

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  • Spectral Theory
  • Resolvent Operator
  • Springer Lecture Note
  • Positive Theory
  • Symmetric Boundary Condition

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References

  1. R. ARENS, Operational calculus of linear relations. Pacific J. Math. 11, 1961, 9–23.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. F.V. ATKINSON, W.N. EVERITT and K.S. ONG, On the m-coefficient of Weyl for a differential equation with an indefinite weight function. To appear in Proc. London Math. Soc.

    Google Scholar 

  3. CHR. BENNEWITZ, Symmetric relations on a Hilbert space. Proc. Conference on the Theory of Ordinary and Partial Differential Equations, Dundee, Scotland, March 1972, Springer Lecture Notes 280, 212–218.

    Google Scholar 

  4. CHR. BENNEWITZ, Spectral theory for pairs of partial differential expressions. Uppsala University, Department of Mathematics, Report 1974:3, 1–4.

    Google Scholar 

  5. CHR. BENNEWITZ, Remarks on the spectral theory for pairs of ordinary differential operators. Uppsala University, Department of Mathematics, Report 1974:4, 1–20.

    Google Scholar 

  6. FRED BRAUER, Spectral theory for the differential equation Lu = λMu. Canad. J. Math. 10, 1958, 431–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W.N. EVERITT, Singular Differential Equations I: The Even Order Case. Math. Ann. 156, 1964, 9–24.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. W.N. EVERITT, Integrable-Square, Analytic Solutions of Odd-Order, Formally Symmetric, Ordinary Differential Equations. Proc. London Math. Soc. Third Series, XXV, July 1972, 156–182.

    Google Scholar 

  9. BERT KARLSSON, Generalization of a theorem of Everitt. To appear in Proc. London Math. Soc.

    Google Scholar 

  10. BERT KARLSSON, A compactness theorem for pairs of formally self-adjoint ordinary differential operators. Uppsala University, Mathematics Department, Report 1974:2, 1–10.

    Google Scholar 

  11. BERT KARLSSON, On the limit circle case for pairs of ordinary symmetric differential operators in a left-positive theory. To appear in Uppsala University, Mathematics Department Report.

    Google Scholar 

  12. H.-D. NIESSEN and A. SCHNEIDER, Integraltransformationen zu singulären S-hermiteschen Rand-Eigenwertproblemen. Manuscripta Math. 5, 1971, 133–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. ÅKE PLEIJEL, Some remarks about the limit point and limit circle theory. Ark. Mat. 7:21, 1968, 543–550.

    MathSciNet  MATH  Google Scholar 

  14. ÅKE PLEIJEL, Complementary remarks about the limit point and limit circle theory. Ark. Mat. 8:6, 1969, 45–47.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. ÅKE PLEIJEL, Spectral theory for pairs of ordinary formally self-adjoint differential operators. Journal Indian Math. Soc. 34, 1970, 259–268.

    MathSciNet  MATH  Google Scholar 

  16. ÅKE PLEIJEL, Green’s functions for pairs of formally selfadjoint ordinary differential operators. Conference on the Theory of Ordinary and Partial Differential Equations, Dundee, Scotland, March 1972, Springer Lecture Notes 280, 131–146.

    Google Scholar 

  17. ÅKE PLEIJEL, Generalized Weyl circles. Conference on the Theory of Ordinary and Partial Differential Equations, Dundee, Scotland, March 1974, Springer Lecture Notes. To appear.

    Google Scholar 

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© 1975 Springer-Verlag

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Pleijel, Å. (1975). A survey of spectral theory for pairs of ordinary 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/BFb0067090

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  • DOI: https://doi.org/10.1007/BFb0067090

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07150-1

  • Online ISBN: 978-3-540-37444-2

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