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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Prediction $ n$ units of time ahead


Authors: Takahiko Nakazi and Katutoshi Takahashi
Journal: Proc. Amer. Math. Soc. 80 (1980), 658-659
MSC: Primary 60G25; Secondary 30D55
DOI: https://doi.org/10.1090/S0002-9939-1980-0587949-1
MathSciNet review: 587949
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Abstract: The purpose of this note is to give a simple expression in terms of w of the quantities

$\displaystyle {\rho _n}(w) = \mathop {\inf }\limits_f \int_0^{2\pi } {\vert 1 + {e^{in\theta }}f{\vert^2}w\,d\theta /2\pi } \quad (n = 0,1,2, \ldots ),$

where f ranges over the analytic trigonometric polynomials with mean value zero and w is nonnegative and summable on the circle.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0587949-1
Keywords: Prediction theory, Szegö's theorem, n units of time ahead, outer function, Fourier coefficients
Article copyright: © Copyright 1980 American Mathematical Society