Approximation Functionals and Their Application

Abstract

The purpose of this work is to obtain local estimates, and to calculate the constants of approximation of smooth functions. To achieve this goal, the trajectory of functionals, the concept of an approximation families of functionals, the tape of the trajectory of functionals and the width of the tape are considered. For this, the concepts of approximation functionals and their trajectories in the conjugate space are introduced, and the concepts of the trajectory tape and the tape width at a given point are discussed. The resulting overall evaluation of the approximation is applied to multidimensional cases, namely, to approximations by the Courant and Zlamal elements.