Abstract
In this paper we present a new proof of the classical Adamyan-Arov-Krein theorem on the approximation of rational functions in Hankel norm. Let y(t), t ϵ Z , be a scalar-valued stationary process. We define a Hankel operator H with singular values which are equal to the canonical correlations between the past and the future of y. We approximate this Hankel operator by H k using a finite-dimensional realization of the process y, and show that the singular values of H k coincide with the canonical correlations between two suitably defined subspaces.
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