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The Landau problem and Kolmogorov’s theorem

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)

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References

  1. A. S. Cavaretta, “An elementary proof of Kolmogorov’s theorem,” Amer. Math. Monthly, 81 (1974), 480–486.

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  2. S. Karlin, “Some variational problems on certain Sobolev spaces and perfect splines,” BAMS, 79 (1973), 124–128.

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  3. A. N. Kolmogorov, “On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval,” Amer. Math. Soc. Trans. Series 1, 2 (1962), 233–243 (Russian, 1939).

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  4. E. Landau, “Einige Ungleichungen für zweimal differenzierbare Funktionen,” Proc. London Math. Soc., (2), 13 (1913), 43–49.

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  5. I. J. Schoenberg and A. S. Cavaretta, “Solution of Landau’s problem concerning higher derivatives on the half line,” MRC Technical Summary Report 1050, Madison, Wisconsin, 1970.

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Fisher, S.D., Jerome, J.W. (1975). The Landau problem and Kolmogorov’s theorem. In: Minimum Norm Extremals in Function Spaces. Lecture Notes in Mathematics, vol 479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097073

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  • DOI: https://doi.org/10.1007/BFb0097073

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