Abstract
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 the information operator is specified by a fixed table of its values. Quadrature formulas for calculating integrals of rapidly oscillating functions have been constructed that are optimal in terms of accuracy and optimal in order of accuracy. The optimal estimates for the error of the method are obtained. Keywords: integrals of rapidly oscillating functions, interpolation classes of functions, quadrature formulas optimal in terms of accuracy, method of boundary functions, lower estimate of numerical integration error.
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