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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1032–1043, August, 2010.
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Vakarchuk, S.B., Doronin, V.G. Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes. Ukr Math J 62, 1199–1212 (2011). https://doi.org/10.1007/s11253-011-0424-0
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DOI: https://doi.org/10.1007/s11253-011-0424-0