APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS

In the class of functions analytic in the annulus $C_r:=\left\{z\in\mathbb{C}\, :\, r<|z|<1\right\}$ with bounded $L^p$-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle $\Gamma_r$ of radius $r$ to values of the derivative of the function on the circle $\Gamma_\rho$ of radius $\rho,\, r<\rho<1,$ by bounded linear operators from $L^p(\Gamma_r)$ to $L^p(\Gamma_ \rho)$ with norms not exceeding a number $N$.  A solution of the problem has been obtained in the case when $N$ belongs to the union of a sequence of intervals. The related problem of optimal recovery of the derivative of a function from boundary values of the function on $\Gamma_\rho$ given with an error has been solved

ON THE 75TH BIRTHDAY OF PROFESSOR VITALII VLADIMIROVICH ARESTOV

July 16, 2018, was the 75th birthday of famous Russian scientist, prominent mathematician, Doctor of Physics and Mathematics, Professor Vitalii Vladimirovich Arestov