Optimal Interpolation on Some Classes of Smooth Functions Defined on the Whole Real Axis

In this paper a new research direction in the optimal interpolation theory is introduced, where the classes of functions to be considered are defined on the whole real axis, and a set of permissible interpolating knots is a denumerable set satisfying certain regular conditions.Some basic problems are formulated, and the exact results obtained in recent years are surveyed.Moreover, many unsolved problems have been put forward.