Vestnik КRAUNC. Fiz.-Mat. nauki. 2022. vol. 40. no. 3. P. 211-226. ISSN 2079-6641

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MSC 65D30, 65D32

Research Article

Optimal quadrature formulas in the space \widetilde{W_2}^{(m,m-1)} of periodic functions

A. R. Hayotov¹², U. N. Khayriev¹

¹V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 4b University str., Tashkent, 100174, Uzbekistan
²National University of Uzbekistan named after Mirzo Ulugbek, 4 University str., Tashkent, 100174, Uzbekistan
E-mail: hayotov@mail.ru,khayrievu@gmail.com

This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space \widetilde{W_2}^{(m,m-1)} of real-valued, periodic functions. For this the extremal function of the quadrature formula is used. In addition, it is shown that the norm of the error functional for the optimal quadrature formula constructed in the space \widetilde{W_2}^{(m,m-1)} is less than the value of the norm of
the error functional for the optimal quadrature formula in the Sobolev space \widetilde{L_2}^{(m)}.

Key words: optimal quadrature formula, optimal coefficients, error of quadrature formula, the Hilbert space, the error functional, Fourier transform.

DOI: 10.26117/2079-6641-2022-40-3-211-226

Original article submitted: 30.07.2022

Revision submitted: 01.11.2022

For citation. Hayotov A. R., Khayriev U. N. Optimal quadrature formulas in the space \widetilde{W_2}^{(m,m-1)} of periodic functions. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 211-226.

DOI: 10.26117/2079-6641-2022-40-3-211-226

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Hayotov A. R., Khayriev U. N., 2022

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

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Hayotov Abdullo Rahmonovich – D. Sci. (Phys. & Math.), Professor, Head of the Laboratory of Computational Mathematics, V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan, ORCID 0000-0002-2756-9542.

Khayriev Umedjon Narmon ugli – PhD Student at the laboratory of Computational Mathematics, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan Laboratory of Computational Mathematics, ORCID 0000-0003-2156-3745.

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