2018
Том 70
№ 4

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

Vakarchuk S. B.

Abstract

Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the best approximation $\mathcal{A}_{\sigma}(f)$ is estimated from above by the averaged smoothness characteristic $\Phi_2(f, t) = \cfrac 1t \int^t_0||\Delta^2_h(f)||dh$. We also calculate the exact values of the average $\nu$-widths of classes of functions defined by $\Phi_2$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 680-692.

Citation Example: Vakarchuk S. B. Best mean-square approximation of functions defined on the real axis by entire functions of exponential type // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 604-615.

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