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

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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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1674–1685, December, 2006.

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Savchuk, V.V. Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials. Ukr Math J 58, 1904–1915 (2006). https://doi.org/10.1007/s11253-006-0175-5

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  • DOI: https://doi.org/10.1007/s11253-006-0175-5

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