A prediction problem in  |
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| Authors: | Mohsen Pourahmadi Akihiko Inoue Yukio Kasahara |
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| Affiliation: | Division of Statistics, Northern Illinois University, DeKalb, Illinois 60115-2854 ; Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan ; Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan |
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| Abstract: | For a nonnegative integrable weight function  on the unit circle  , we provide an expression for  , in terms of the series coefficients of the outer function of  , for the weighted  distance  , where  is the normalized Lebesgue measure and  ranges over trigonometric polynomials with frequencies in ![$ [{dots,-3,-2,-1}setminus{-n}]cup{m}$](http://www.ams.org/proc/2007-135-04/S0002-9939-06-08575-3/gif-abstract0/img9.gif) ,  ,  . The problem is open for  . |
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| Keywords: | Duality and orthogonalization extremal problems stationary processes |
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