单词 | Landau-Kolmogorov Constants | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
释义 | Landau-Kolmogorov ConstantsN.B. A detailed on-line essay by S. Finchwas the starting point for this entry. Let
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For a real-valued function
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Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/lk/lk.html Franco, Z. M.; Kaper, H. G.; Kwong, M. N.; and Zettl, A. ``Bounds for the Best Constants in Landau's Inequality on the Line.'' Proc. Roy. Soc. Edinburgh 95A, 257-262, 1983. Franco, Z. M.; Kaper, H. G.; Kwong, M. N.; and Zettl, A. ``Best Constants in Norm Inequalities for Derivatives on a Half Line.'' Proc. Roy. Soc. Edinburgh 100A, 67-84, 1985. Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities. Cambridge, England: Cambridge University Press, 1934. Kolmogorov, A. ``On Inequalities Between the Upper Bounds of the Successive Derivatives of an Arbitrary Function on an Infinite Integral.'' Amer. Math. Soc. Translations, Ser. 1 2, 233-243, 1962. Kupcov, N. P. ``Kolmogorov Estimates for Derivatives in Kwong, M. K. and Zettl, A. Norm Inequalities for Derivatives and Differences. New York: Springer-Verlag, 1992. Landau, E. ``Einige Ungleichungen für zweimal differentzierbare Funktionen.'' Proc. London Math. Soc. Ser. 2 13, 43-49, 1913. Landau, E. ``Die Ungleichungen für zweimal differentzierbare Funktionen.'' Danske Vid. Selsk. Math. Fys. Medd. 6, 1-49, 1925. Ljubic, J. I. ``On Inequalities Between the Powers of a Linear Operator.'' Amer. Math. Soc. Trans. Ser. 2 40, 39-84, 1964. Neta, B. ``On Determinations of Best Possible Constants in Integral Inequalities Involving Derivatives.'' Math. Comput. 35, 1191-1193, 1980. Schoenberg, I. J. ``The Elementary Case of Landau's Problem of Inequalities Between Derivatives.'' Amer. Math. Monthly 80, 121-158, 1973. |
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