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Real, complex and functional analysis
The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions
V. L. Vaskevichab a Sobolev Institute of Mathematics,
pr. Koptyuga, 4,
630090, Novosibirsk, Russia
b Novosibirsk State University,
Pirogova, 2,
630090, Novosibirsk, Russia
Abstract:
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.
Received August 28, 2018, published October 5, 2018
Citation:
V. L. Vaskevich, “The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions”, Sib. Èlektron. Mat. Izv., 15 (2018), 1080–1090
Linking options:
https://www.mathnet.ru/eng/semr981 https://www.mathnet.ru/eng/semr/v15/p1080
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Statistics & downloads: |
Abstract page: | 167 | Full-text PDF : | 21 | References: | 16 |
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