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

Abstract

In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral ${\int }_a^b{e}^{2\pi i\omega x}\phi (x)dx$ with $\omega \in \mathbb{R}$ 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.

arXiv admin note: substantial text overlap with arXiv:2001.02636

References in corpus (2)

• Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space
• On an optimal quadrature formula for approximation of Fourier integrals in the space $W_2^{(1,0)}$

Cited by in corpus (1)

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