Geodesic
About three-dimensional nets of Smolyak III
Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 249-254

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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. 
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     title = {About three-dimensional nets of {Smolyak} {III}},
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N. N. Dobrovol'skii; D. V. Gorbachev; V. I. Ivanov. About three-dimensional nets of Smolyak III. Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 249-254. http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a18/