Reconstruction of Hp -Functions: Best Approximation, Regularization and Optimal Error Estimates

Abstract

Let U be the open unit disc of the complex plane. We explicitly construct the best pointwise approximation for determining a function in the Hardy space H p (U) from measured data at a countable set of points in U whenever the data is exact. A regularization scheme is given to deal with the case of nonexact data. Moreover, optimal error estimates are also studied.