LINEAR METHODS FOR APPROXIMATION OF SOME CLASSES OF HOLOMORPHIC FUNCTIONS FROM THE BERGMAN SPACE

We construct a linear method {Q(n,psi)}(n is an element of N) for the approximation (in the unit disk) of classes of holomorphic functions A(p)(psi) that are the Hadamard convolutions of the unit balls of the Bergman space A(p) with reproducing kernels psi(Z) = Sigma(infinity)(k=0) psi(Zk)(k). We give conditions for psi under which the method {Q(n,psi)}(n is an element of N) approximates the class A(p)(psi) in the metrics of the Hardy space H(s) and the Bergman space A(s), 1 <= s <= p, with an error that coincides in order with the value of the best approximation by algebraic polynomials.