AN EXPONENTIALLY WEIGHTED OPTIMAL QUADRATURE FORMULA IN THE SPACE (1,0) W 2 OF PERIODIC FUNCTIONS - Khayriev U.N (SAMARALI TA’LIM VA BARQAROR INNOVATSIYALAR JURNALI, 2024)
This work studies the problem of construction of the optimal quadrature formula in the sense of Sard in the Hilbert space W (1,0) 2  0,1  of periodic, complex-valued functions for numerical calculation of Fourier integrals. Here a quadrature sum consists of a linear combination of the given function values on a uniform mesh. The optimal quadrature formula is obtained by minimizing the norm of the error functional with respect to coefficients.