Best linear methods of approximation and optimal orthonormal systems of the Hardy space - Savchuk, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We construct the best linear methods of the approximation of functions from the Hardy space Hp on compact subsets of the unit disk. We show that the Takenaka - Malmquist systems are such systems of functions that are orthonormal on the unit circle and optimal for the construction of the best linear methods of approximation.