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A Note on the Least Constant in Landau Inequality on a Finite Interval

  • A. Yu. Shadrin
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

In the Landau inequality on the unit interval
$$\parallel f^{(k)}\parallel_{q}\leq \alpha \parallel f\parallel _{p}+\beta \parallel f^{(n)}\parallel _{r}$$
with ∥ · ∥ s := ∥ · ∥ L s[0,1], 1 ≥ p, q, r ≥ ∞, 0 ≥ k < n, we find the least value A 0 of the first constant α.

Key words and phrases

Landau inequality Markov inequality, Lagrange interpolation 

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References

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    V. I. Burenkov, On sharp constants in inequalities between norms of intermediate derivatives on a finite interval, Trudy Mat. Inst. AN SSSR (Proc. Steklov Math. Inst.) 156 (1980), 22–29. (Russian)MathSciNetzbMATHGoogle Scholar
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    H. Kallioniemi The Landau problem on compact intervals and optimal numerical differentiation, J. Approx. Theory 63 (1990), 72–91.MathSciNetzbMATHCrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • A. Yu. Shadrin
    • 1
  1. 1.Computing Center, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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