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Minimization and interpolation at integer points of the real axis

Part VII. Perfect Spline Solutions in the Theory of Best Approximation in L∞

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Part of the Lecture Notes in Mathematics book series (LNM,volume 479)

Keywords

  • Periodic Solution
  • Positive Measure
  • Integer Point
  • Consecutive Interval
  • Power Growth

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References

  1. A. Cavaretta, “Perfect splines of minimal sup norm on the real axis,” J. Approximation Theory 8 (1973), 285–303.

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  2. J. Favard, “Application de la formule sommatorie d’Euler à la demonstration de quelques propriétés extrémales des integrales des fonctions périodiques ou presque-périodiques,” Matematisk Tidsskrift, Ser. B (1936), 81–94.

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  3. S. D. Fisher and J. W. Jerome, “The Euler spline and minimization and interpolation at integer points of the line and half-line,” manuscript.

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  4. S. Karlin, Total Positivity, Vol. 1, Stanford University Press, Stanford, California, 1968.

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  5. I. J. Schoenberg, “The elementary cases of Landau’s problem of inequalities between derivatives,” Amer. Math. Monthly 80 (1973), 121–158.

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  6. -, “Cardinal interpolation and spline functions, II. Interpolation of data of power growth,” J. Approximation Theory 6 (1972), 404–420.

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  7. I. J. Schoenberg, “Cardinal Spline Interpolation,” SIAM, Philadelphia, Pa., 1973.

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  8. J. N. Subbotin, “On the relation between finite differences and the corresponding derivatives, Proc. Steklov Inst. Math. 78 (1965), 24–42. Amer. Math. Soc. Translations (1967).

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© 1975 Springer-Verlag

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Fisher, S.D., Jerome, J.W. (1975). Minimization and interpolation at integer points of the real axis. In: Minimum Norm Extremals in Function Spaces. Lecture Notes in Mathematics, vol 479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097072

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  • DOI: https://doi.org/10.1007/BFb0097072

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07394-9

  • Online ISBN: 978-3-540-37599-9

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