A duality method in prediction theory of multivariate stationary sequences
Michael Frank, Lutz Klotz · Mathematische Nachrichten · 2002
Let W be an integrable positive Hermitian q × q–matrix valued function on the dual group of a discrete abelian group G such that W–1 is integrable. Generalizing results of T. Nakazi [N] and of A. G. Miamee and M. Pourahmadi [MiP] for q = 1 we establish a correspondence between trigonometric approximation problems in L2(W) and certain approximation problems in L2(W–1). The result is applied to prediction problems for q–variate stationary processes over G, inparticular, to the case G = ℤ.