Best linear methods of approximation and optimal orthonormal systems of the Hardy space
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.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 5, pp 730-743.
Citation Example: Savchuk V. V. Best linear methods of approximation and optimal orthonormal systems of the Hardy space // Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 636–646.