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Variation diminishing transformations andSturm-Liouville systems

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Commentarii Mathematici Helvetici

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References

  1. E. A. Coddington andN. Levinson: «Theory of Ordinary Differential Equations», New York, 1955.

  2. F. R. Gantmacher andM. G. Krein: «Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme», Berlin 1960.

  3. I. I. Hirschman Jr.: «Variation diminishing Hankel transforms», J. d’analyse Math. 8 (1960–61), pp. 307–336.

    Article  MathSciNet  Google Scholar 

  4. I. I. Hirschman Jr.: «Variation diminishing transformations and ultraspherical polynomials», J. d’Analyse Math. 8 (1960–61), pp. 337–360.

    MathSciNet  Google Scholar 

  5. I. I. Hirschman Jr.: «Variation diminishing transformations and orthogonal polynomials», to appear in J. d’Analyse Math.

  6. I. I. Hirschman Jr. andD. V. Widder: «The Convolution Transform», Princeton 1955.

  7. S. Karlin andJ. McGregor: «Coincidence properties of birth and death processes», Pacific Jour. of Math. 9 (1959), pp. 1109–1140.

    MathSciNet  MATH  Google Scholar 

  8. N. Levinson: «On the uniqueness of the potential in aSchrödinger equation for a given asymptotic phase», Matematisk-Fysiske Meddelelser, 25 (1949), no. 10.

    Google Scholar 

  9. I. J. Schoenberg: «On Pólya frequency functions, I», J. d’Analyse Math. 1 (1951), pp. 33–374.

    MathSciNet  Google Scholar 

  10. I. J. Schoenberg: «On Pólya frequency functions, II», Acta Sci. Math. Szeged, 12 (1950), 97–106.

    MathSciNet  Google Scholar 

  11. I. J. Schoenberg: «On totally positive functions, Laplace integrals and entire functions of Laguerre-Pólya-Schur type», Proc. Nat. Acad. Sci. U.S.A., 33 (1947), pp. 11–17.

    Article  MathSciNet  MATH  Google Scholar 

  12. I. J. Schoenberg: «On variation diminishing integral operators of the convolution type», Proc. Nat. Acad. Sci. U.S.A., 34 (1948), pp. 164–159.

    Article  MathSciNet  MATH  Google Scholar 

  13. E. C. Titchmarsh: «Eigenfunction Expansions Associated with Second-order Differential Equations», Oxford 1946.

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Authors
  1. I. I. Hirschman Jr.
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Additional information

This work was carried out while the author was in residence in Zurich, and was supported by the United States Air Force through the Air Force Office of Scientific Research and Development Command under Contract No. AF 49 (638)-846.

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Hirschman, I.I. Variation diminishing transformations andSturm-Liouville systems. Commentarii Mathematici Helvetici 36, 214–233 (1962). https://doi.org/10.1007/BF02566900

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  • DOI: https://doi.org/10.1007/BF02566900

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