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

Author： Savchuk V.  

Publisher： Springer Publishing Company

ISSN： 0041-5995

Source： Ukrainian Mathematical Journal, Vol.58, Iss.12, 2006-12, pp. : 1904-1915

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Abstract

On concentric circles T = {z ∈ : ∣z∣ = }, 0 ≤  < 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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