Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space

02/15/2021

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by   A. R. Hayotov, et al.

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In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral ∫_a^b e^2π iω xφ(x)d x with ω∈ℝ in the Hilbert space W_2^(2,1)[a,b] of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.