Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions

We consider the problem of analytic continuation with inaccurate data from a finite subset $U$ of a domain $D$ of $\mathbb{C}^n$ to a point $z_0\in D\setminus U$ функции $f$ из $H(D)$ for the functions f belonging to a bounded correctness set $V$ in a Hilbert space $H(D)$ of analytic functions in $D$. In the case when $H(D)$ is a Hilbert space with a reproducing kernel, we find constructive formulas for calculating the optimal error, the optimal function, and the optimal linear algorithm for extrapolation to a point $z_0$ for functions in $V$ whose approximate values are given on a set $U$. Moreover, we study the asymptotics of the optimal error in the case when the errors of initial data vanish