Best approximation of analytic functions from information about their values at a finite number of points

Abstract

For a class of bounded and analytic functions defined in a simply connected region we construct the best linear method of approximation with respect to information about the values of the function at some points of the region. We show it is unique. We obtain limiting relations for the lower bound of the norm of the error of the best method on an arbitrary compacta with connected complement where the lower bound is taken with respect to nodes from the region of analyticity.