OPTIMAL RECOVERY OF A DERIVATIVE OF AN ANALYTIC FUNCTION FROM VALUES OF THE FUNCTION GIVEN WITH AN ERROR ON A PART OF THE BOUNDARY

We study several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Gamma, in particular, the problem of optimal recovery of the derivative at a point z(0) is an element of G from limit boundary values given with an error on a measurable part gamma(1) of the boundary Gamma for the class Q of functions with limit boundary values bounded by 1 on gamma(0) = Gamma\gamma(1) as well as the problem of the best approximation of the derivative at a point z(0) is an element of G by bounded linear functionals in L-infinity(gamma(1)) on the class Q.