Optimal recovery of the derivative of periodic analytic functions from Hardy classes

Let S beta : = {z is an element of C : \Im z\ < beta}. For 2 pi-periodic fu nctions which are analytic in S-beta with p-integrable boundary values, at construct an optimal method of recovery of f4(xi), xi is an element of S-be ta, using information about the values f(x(1)), ..., f(x(n)), x(j) is an el ement of [0, 2 pi). (C) 1999 Academic Press.