Geodesic
Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 211-226

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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 $\widetilde{L_2}^{(m)}$.
Keywords: the Hilbert space, the error functional
Mots-clés : optimal quadrature formula, optimal coefficients, error of quadrature formula, Fourier transform. 
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     author = {A. R. Hayotov and U. N. Khayriev},
     title = {Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {211--226},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a16/}
}
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A. R. Hayotov; U. N. Khayriev. Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 211-226. http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a16/