A prediction problem in 𝐿²(𝑤)

Pourahmadi, Mohsen; Inoue, Akihiko; Kasahara, Yukio

doi:10.1090/S0002-9939-06-08575-3

A prediction problem in $L^2 (w)$
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by Mohsen Pourahmadi, Akihiko Inoue and Yukio Kasahara

Proc. Amer. Math. Soc. 135 (2007), 1233-1239

DOI: https://doi.org/10.1090/S0002-9939-06-08575-3

Published electronically: October 18, 2006

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Abstract:

For a nonnegative integrable weight function $w$ on the unit circle $T$, we provide an expression for $p=2$, in terms of the series coefficients of the outer function of $w$, for the weighted $L^p$ distance $\inf _f \int _T|1-f|^p wd \mu$, where $\mu$ is the normalized Lebesgue measure and $f$ ranges over trigonometric polynomials with frequencies in $[\{\dots ,-3,-2,-1\}\setminus \{-n\}]\cup \{m\}$, $m \geq 0$, $n \geq 2$. The problem is open for $p \neq 2$.

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