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

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Ukrainian Mathematical Journal Aims and scope

Exact constants in Jackson-type inequalities are calculated in the space L 2.(ℝ) in the case where the quantity of the best approximation A σ (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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  1. Nobel Dnepropetrovsk University, Dnepropetrovsk, Ukraine

    S. B. Vakarchuk

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Vakarchuk, S.B. Best mean-square approximation of functions defined on the real axis by entire functions of exponential type. Ukr Math J 64, 680–692 (2012). https://doi.org/10.1007/s11253-012-0671-8

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  • DOI: https://doi.org/10.1007/s11253-012-0671-8

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