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 commentarXiv admin note: substantial text overlap with arXiv:2001.02636

References in corpus (4)

• Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space
• Complexity of Oscillatory Integration for Univariate Sobolev Spaces
• Optimal Quadrature Formulas for the Sobolev Space $H^1$
• 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