Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems

In this paper with the help of Smolyak quadrature formulas we calculate exact orders of errors of the numerical integration of trigonometric Fourier coefficients of functions from generalized classes of the Korobov and Sobolev type. We apply the obtained results to the recovery of functions from their values at a finite number of points in terms of K. Sherniyazov approach.