On the Szegő—Kolmogorov prediction theorem

The classical Szegő—Kolmogorov theorem characterizes the weights ω such that family of exponentials with positive integer frequencies spans whole weighted space \({L^2}(\mathbb{T},w)\) on circle. Kolmogorov’s probabilistic interpretation this result connects it possibility to ‘predict precisely future from past’ for stationary stochastic processes discrete time. We discuss problem whether prediction remains possible if some part ‘past’ is not known.