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A Duality Method in Prediction Theory of Multivariate Stationary Sequences
Author(s) -
Frank Michael,
Klotz Lutz
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200210)244:1<64::aid-mana64>3.0.co;2-p
Subject(s) - mathematics , integrable system , abelian group , hermitian matrix , trigonometry , group (periodic table) , locally integrable function , pure mathematics , matrix (chemical analysis) , combinatorics , mathematical physics , mathematical analysis , physics , quantum mechanics , materials science , composite material
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 L 2 ( W ) and certain approximation problems in L 2 ( W –1 ). The result is applied to prediction problems for q –variate stationary processes over G , inparticular, to the case G = ℤ.