Optimal quadrature and cubature formulas for computing Fourier transform of finite functions of one class. Case of strong oscillation

The paper deals with quadrature and cubature formulas, optimal and nearly optimal in accuracy, used to evaluate integrals of quickly oscillating functions in a class of bounded functions with piecewise continuous first derivatives bounded by a constant in one-and multidimensional cases. Optimal estimates for the numerical integration error and upper bounds are obtained for these integrals in case of strong oscillation of subintegral functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 144–164, September–October 2007.