optimal quadrature formula, optimal coefficients, error of quadrature formula, the hilbert space, the error functional, fourier transform, оптимальная квадратурная формула, оптимальные коэффициенты, погрешность квадратурной формулы, гильбертово пространство, функционал погрешности, преобразование фурье, Science

This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space W2​​(m,m−1) of real-valued, periodic functions. For this the extremal function of the quadrature formula is used. In addition, it is shown that the norm of the error functional for the optimal quadrature formula constructed in the space W2​​(m,m−1)is less than the value of the norm of the error functional for the optimal quadrature formula in the Sobolev space L2​​(m).