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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1080–1090 (Mi semr981)  

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.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.5., проект № 0314-2016-0013


DOI: https://doi.org/10.17377/semi.2018.15.090

Full text: PDF file (169 kB)
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Document Type: Article
UDC: 517.518.23
MSC: 65D32
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

Citation in format AMSBIB
\Bibitem{Vas18}
\by V.~L.~Vaskevich
\paper The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1080--1090
\mathnet{http://mi.mathnet.ru/semr981}
\crossref{https://doi.org/10.17377/semi.2018.15.090}


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