Geodesic
On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 591-620

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We solve the problem of the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for the following classes of differentiable periodic functions: $W^r$ ($r>3$), $W^rH_\omega$ (where $\omega$ is a convex modulus of continuity and $r$ is odd), and $W^rL$ ($r=4,6,\dots$). 
@article{IM2_1974_8_3_a8,
     author = {V. P. Motornyi},
     title = {On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions},
     journal = {Izvestiya. Mathematics },
     pages = {591--620},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/}
}
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V. P. Motornyi. On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 591-620. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a8/