Geodesic
Convergence of cubature formulas of high trigonometric precision in multidimensional periodic Sobolev spaces
Matematičeskie trudy, Tome 18 (2015) no. 1, pp. 3-14

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We establish convergence in a norm of cubature formulas of high trigonometric precision on multidimensional periodic Sobolev spaces including spaces of fractional smoothness. The main result is obtained under the conventional conditions on smoothness of the space of integrands and distribution of the nodes of the cubature formulas. 
@article{MT_2015_18_1_a0,
     author = {V. L. Vaskevich},
     title = {Convergence of cubature formulas of high trigonometric precision in multidimensional periodic {Sobolev} spaces},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2015_18_1_a0/}
}
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V. L. Vaskevich. Convergence of cubature formulas of high trigonometric precision in multidimensional periodic Sobolev spaces. Matematičeskie trudy, Tome 18 (2015) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/MT_2015_18_1_a0/