Best and optimal recovery methods for classes of harmonic functions

The author considers problems of best recovery of a functional $L_u=\lambda_0u(x)+\dots+\lambda_ku^{(k)}(x)$, $x\in(-1,1)$, in the space $h_p$ of harmonic functions for $p=\infty$ or 2, in terms of the values of the functions and their derivatives at points of the interval $(-1,1)$. In the space $h_\infty$ the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.