On optimal recovery methods in Hardy-Sobolev spaces

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