On optimal recovery methods in Hardy–Sobolev spaces

A general approach to the construction of optimal methods of recovery of linear functionals from a known solution of the dual extremal problem is proposed which is based on a certain parametrization of this solution of the dual problem. Using this approach several optimal recovery problems in Hardy–Sobolev classes are successfully solved, including the recovery of functions from information about their Fourier coefficients or about the values of the function at some system of nodes, in the periodic and non-periodic cases.