Recovery and integration of functions from the Korobovs anisotropic class

The problem of approximate recovery of functions from the class $E^{r_1\dots,r_s}$ by means of an operator in the form of ал algebraic polynomial is considered. The algorithm based on application of the theory of divisors in cyclotomic fields of the algebraic integers is applied to determination of optimum factors of an operator. The problem of approximate integration of functions from the class $E^{r_1\dots,r_s}$ in the domain distinct from $[0,1]^s$ is considered.