2017
Том 69
№ 9

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

Abstract

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 $Ω_1(f, t ),\; t > 0$, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean $ν$-width, $ν > 0$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 8, pp 1199-1212.

Citation Example: Doronin V. G., Vakarchuk S. B. Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes // Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1032–1043.

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