About three-dimensional nets of Smolyak III
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:
1. the linear operator 𝐴𝑞 of weighted grid averages over the Smolyak grid at dimension 𝑠 > 3
is not normal;
2. found the values of some trigonometric sums 𝑆𝑞(𝑚1, . . . ,𝑚𝑠) of the resin grid at the dimension 𝑠 >= 3.
About the Authors
Nikolai Nikolaevich Dobrovol’skii
Tula State University, Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Dmitry Viktorovich Gorbachev
Tula State
University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Valerii Ivanovich Ivanov
Tula State
University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
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13. Ph.D. Thesis, Moscow State University, Moscow, Russia.
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Review
For citations:
Dobrovol’skii N.N., Gorbachev D.V., Ivanov V.I. About three-dimensional nets of Smolyak III. Chebyshevskii Sbornik. 2022;23(3):249-254. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-3-249-254
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