Optimal Recovery of the Derivative of Periodic Analytic Functions from Hardy Classes Original Research Article

LetSβ≔{z∈C: |Im z|<β}. For 2π-periodic functions which are analytic inSβwithp-integrable boundary values, we construct an optimal method of recovery off′(ξ), ξ∈Sβ, using information about the valuesf(x1), mldr;, f(xn), xj∈[0, 2π).