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arXiv · 2102.07551

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

A. R. Hayotov·S. S. Babaev
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Abstract

In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_a^b e^{2πiωx}φ(x)d x$ with $ω\in \mathbb{R}$ 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.

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A. R. Hayotov, S. S. Babaev. 2021-02-15. Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space. https://doi.org/10.1063/5.0057127

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