2017
Том 69
№ 6

All Issues

Linear methods for approximation of some classes of holomorphic functions from the Bergman space

Savchuk V. V.

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Abstract

We construct a linear method of the approximation $ \{Q_{n,\psi} \}_{n \in {\mathbb N}}$ in the unit disk of classes of holomorphic functions $A^{\psi}_p$ that are the Hadamard convolutions of unit balls of the Bergman space $A_p$ with reproducing kernels $\psi(z) = \sum^\infty_{k=0}\psi_k z^k.$ We give conditions on $\psi$ under which the method $ \{Q_{n,\psi} \}_{n \in {\mathbb N}}$ approximate the class $A^{\psi}_p$ in metrics of the Hardy space $H_s$ and Bergman space $A_s,\; 1 \leq s \leq p,$ with error that coincides in order with a value of the best approximation by algebraic polynomials.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 6, pp 910-926.

Citation Example: Savchuk V. V. Linear methods for approximation of some classes of holomorphic functions from the Bergman space // Ukr. Mat. Zh. - 2008. - 60, № 6. - pp. 783–795.

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