Geodesic
The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1080-1090

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A power-law order of convergence to zero of a sequence of norms of error functionals for minimal and almost minimal cubature formulas is established. Functionals act on multidimensional periodic Sobolev spaces, including on spaces with fractional smoothness.
Keywords: cubature formulas, minimal and almost minimal cubature formulas, the convergence order, error functionals, extremal functions, embedding constants. 
@article{SEMR_2018_15_a135,
     author = {V. L. Vaskevich},
     title = {The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1080--1090},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a135/}
}
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V. L. Vaskevich. The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1080-1090. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a135/