Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 680–692 | Cite as

Best mean-square approximation of functions defined on the real axis by entire functions of exponential type

  • S. B. Vakarchuk
Article
Exact constants in Jackson-type inequalities are calculated in the space L2.(ℝ) in the case where the quantity of the best approximation Aσ (f) is estimated from above by the averaged smoothness characteristic
$$ {\varPhi_2}\left( {f,t} \right)=\frac{1}{t}\int\limits_0^t {\left\| {\Delta_h^2(f)} \right\|dh} $$
.

We also calculate the exact values of the average v-widths of classes of functions defined by Φ2.

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 604–615, May, 2012.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  1. 1.Nobel Dnepropetrovsk UniversityDnepropetrovskUkraine

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