Some remarks on an interpolation problem of A. M. Yaglom

The paper deals with the problem of best mean-square interpolation of a continuous q-variate weakly stationary random process x over R on the basis of the values x (k), k epsilon Z; which was studied first by A. M. Yaglom (Uspehi Matem. Nauk (N.S.), 4 (1949), pp. 173-178 (in Russian)] in the case q = 1. For the family J(Z) of all subsets of R which are shifts of Z, criterions of J(Z)-singularity and,J(Z)-regularity in terms of the nonstochastic spectral measure of x are given. Related results for stationary sequences over Z are stated.