2017
Том 69
№ 7

All Issues

Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials

Savchuk V. V.

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Abstract

On concentric circles $T_{ϱ} = {z ∈ ℂ: ∣z∣ = ϱ},\; 0 ≤ ϱ < 1$, we determine the exact values of the quantities of the best approximation of holomorphic functions of the Bergman class $A_p, 2 ≤ p ≤ ∞$, in the uniform metric by algebraic polynomials generated by linear methods of summation of Taylor series. For $1 ≤ p < 2$, we establish exact order estimates for these quantities.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 12, pp 1904-1915.

Citation Example: Savchuk V. V. Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials // Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1674–1685.

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