Optimal Recovery of a Derivative of an Analytic Function from Values of the Function Given with an Error on a Part of the Boundary

Abstract

We study several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Γ, in particular, the problem of optimal recovery of the derivative at a point z0 ∈ G from limit boundary values given with an error on a measurable part γ1 of the boundary Γ for the class Q of functions with limit boundary values bounded by 1 on γ0 = Γ\γ1 as well as the problem of the best approximation of the derivative at a point z0 ∈ G by bounded linear functionals in L∞ (γ1) on the class Q.