About three-dimensional nets of Smolyak III

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 $s\ge3$.