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

  • V. V. Savchuk


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.
How to Cite
Savchuk, V. V. “Linear Methods for Approximation of Some Classes of Holomorphic Functions from the Bergman Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 6, June 2008, pp. 783–795,
Research articles