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Ukrainian Mathematical Journal

, Volume 62, Issue 8, pp 1199–1212 | Cite as

Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes

  • S. B. Vakarchuk
  • V. G. Doronin
Article

We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree ≤ σ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics Ω1(f, t ), t > 0, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean ν-width, ν > 0.

Keywords

Entire Function Functional Classis Nonnegative Function Cubature Formula Arbitrary Positive Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  • V. G. Doronin
    • 2
  1. 1.Dnepropetrovsk University of Economics and LawDnepropetrovskUkraine
  2. 2.Gonchar Dnepropetrovsk National UniversityDnepropetrovskUkraine

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