On the Szegő—Kolmogorov prediction theorem

Alexander Olevskii, Alexander Ulanovskii*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The classical Szegő—Kolmogorov theorem characterizes the weights ω such that the family of exponentials with positive integer frequencies spans the whole weighted space L2(T, w) on the circle. Kolmogorov’s probabilistic interpretation of this result connects it with the possibility to ‘predict precisely the future from the past’ for the stationary stochastic processes with discrete time. We discuss the problem whether the prediction remains possible if some part of the ‘past’ is not known.

Original languageEnglish
Pages (from-to)335-351
Number of pages17
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Dec 2021


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