BEST AND OPTIMAL RECOVERY METHODS FOR CLASSES OF HARMONIC FUNCTIONS

Abstract

The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space 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.