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Bernstein-type inequalities for splines defined on the real axis

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We obtain exact Bernstein-type inequalities for splines \( s \in {S_{m,h}}\bigcap {{L_2}\left( \mathbb{R} \right)} \), as well as the exact inequalities estimating, for splines sS m, h , h > 0; the L p -norms of the Fourier transforms of their kth derivative in terms of the L p -norms of the Fourier transforms of the splines themselves.

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Author information

Correspondence to V. F. Babenko.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 5, pp. 603–611, May, 2011.

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Babenko, V.F., Zontov, V.A. Bernstein-type inequalities for splines defined on the real axis. Ukr Math J 63, 699–708 (2011). https://doi.org/10.1007/s11253-011-0536-6

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  • Real Axis
  • Approximation Theory
  • Ukrainian National Academy
  • Polynomial Spline
  • Linear Partial Differential Operator