Some problems in approximation theory for a class of functions of finite smoothness

This paper concerns the problem of best accuracy in recovering functions from their values at a specified number of points, the problem of best approximation of partial differential operators by bounded operators, and the problem of the accuracy of approximation of one class by another for a class of functions with partial derivatives of a fixed order having moduli of continuity not exceeding a given modulus of continuity. The weak asymptotic behavior is established for the corresponding quantities.