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On variation diminishing transformations on the circle

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References

  1. F. Gantmakher and M. Krein,Oscillatory matrices and kernels and small vibrations of mechanical systems (in Russian), 2nd Ed. Moscow, 1950.

  2. I. I. Hirschman and D. V. Widder,The convolution transform, Princeton, 1955.

  3. S. Karlin and J. McGregor,Coincidence probabilities, Technical Report No. 8 (November 17, 1958), Stanford University, Stanford, California.

    Google Scholar 

  4. I. P. Natanson,Konstruktive Funktionentheorie (Translation from Russian), Berlin, 1955.

  5. G. Pólya and G. Szegö,Aufgaben und Lehrsätze aus der Analysis, vol. 2, Berlin, 1925.

  6. G. Pólya,Qualitatives über Wärmeausgleich, Zeitschrift für angew. Math. und Mech., vol. 13 (1933), pp. 125–128.

    Article  MATH  Google Scholar 

  7. G. Pólya and I. J. Schoenberg,Remarks on de la Vallée Poussin means and convex conformal maps of the circle, Pacific J. of Math., vol. 8 (1958), pp. 295–334.

    MATH  Google Scholar 

  8. I. J. Schoenberg and Anne Whitney,A theorem on polygons in n dimensions with applications ..., Compositio Math., vol. 9 (1951), pp. 141–160.

    MATH  MathSciNet  Google Scholar 

  9. I. J. Schoenberg,On Pólya frequency functions, I, J. d'Analyse Math., vol. 1 (1951). pp.331–374.

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  11. I. J. Schoenberg,On smoothing operations and their generating functions, Bull. Amer. Math., Soc. vol. 59 (1953), pp. 199–230.

    Article  MATH  MathSciNet  Google Scholar 

  12. I. J. Schoenberg,An isoperimetric inequality for closed curves convex in even-dimensional Euclidean spaces, Acta Math., vol. 91 (1954), pp. 143–164.

    Article  MATH  MathSciNet  Google Scholar 

  13. Ch. J. de la Vallée Poussin,Sur l'approximation des fonctions d'une variable réelle et de leurs dérivées par des polynomes et des suites limitées de Fourier, Bull. de l'Acad. roy. de Belgique (Classe des sciences), No. 3, pp. 193–254 (1908).

    Google Scholar 

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Authors and Affiliations

  1. Durham, N. H., U.S.A.

    J. C. Mairhuber, I. J. Schoenberg & R. E. Williamson

  2. Philadelphia, Pa., U.S.A.

    J. C. Mairhuber, I. J. Schoenberg & R. E. Williamson

  3. Hanover, N. H., U.S.A.

    J. C. Mairhuber, I. J. Schoenberg & R. E. Williamson

Authors
  1. J. C. Mairhuber
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  2. I. J. Schoenberg
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  3. R. E. Williamson
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Additional information

This paper was prepared partly under the sponsorship of the United States Air Force, Offfce of Scientific Research, ARDC, under a contract with the University of Pennsylvania.

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Mairhuber, J.C., Schoenberg, I.J. & Williamson, R.E. On variation diminishing transformations on the circle. Rend. Circ. Mat. Palermo 8, 241–270 (1959). https://doi.org/10.1007/BF02843691

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  • DOI: https://doi.org/10.1007/BF02843691

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