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Chebyshevskii Sbornik, 2022, Volume 23, Issue 3, Pages 249–254
DOI: https://doi.org/10.22405/2226-8383-2022-23-3-249-254 (Mi cheb1211) 		 
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About three-dimensional nets of Smolyak III

N. N. Dobrovol'skiiab, D. V. Gorbachevb, V. I. Ivanovb

a Tula State Lev Tolstoy Pedagogical University (Tula)
b Tula State University (Tula)
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DOI: https://doi.org/10.22405/2226-8383-2022-23-3-249-254
Abstract: This is the third article in a series dedicated to Smolyak grids. The work relates to analytical number theory and it deals with the application of number theory to problems of approximate analysis. The paper shows that:
  • the linear operator $A_{q}$ of weighted grid averages over the Smolyak grid at dimension $s\ge3$ is not normal;
  • found the values of some trigonometric sums $S_{q}(m_1,\ldots,m_s)$ of the resin grid at the dimension $s\ge3$.
Keywords: grid Smolyak, quadrature formulas with grids of Smolyak, interpolation formula with grids of Smolyak.
Funding agency Grant number
Russian Foundation for Basic Research 19-41-710005_р_а
Acknowledgments: The reported study was funded by RFBR, project number 19-41-710005_r_a. The study was carried out at the expense of a grant from the Government of the Tula region (contract No. DS/306 dated 11/16/2021).
Received: 11.06.2022
Accepted: 14.09.2022
Document Type: Article
UDC: 511.3
Language: Russian
Citation: N. N. Dobrovol'skii, D. V. Gorbachev, V. I. Ivanov, “About three-dimensional nets of Smolyak III”, Chebyshevskii Sb., 23:3 (2022), 249–254
Citation in format AMSBIB
\Bibitem{DobGorIva22}
\by N.~N.~Dobrovol'skii, D.~V.~Gorbachev, V.~I.~Ivanov
\paper About three-dimensional nets of Smolyak III
\jour Chebyshevskii Sb.
\yr 2022
\vol 23
\issue 3
\pages 249--254
\mathnet{http://mi.mathnet.ru/cheb1211}
\crossref{https://doi.org/10.22405/2226-8383-2022-23-3-249-254}
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