Optimal Calculation of Integrals of Rapidly Oscillating Functions for Some Classes of Differential Functions

The author considers the problem of calculating integrals of rapidly oscillating functions from some classes of differential functions, in particular, in the case of the interpolation class of functions, where a fixed table of its values specifies the information operator. Quadrature formulas for calculating integrals of rapidly oscillating functions that are optimal in terms of accuracy and in the order of accuracy are constructed. The optimal estimates for the error of the method are obtained.