By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: (n = 0,±1,...) The paper deals with prediction problems for sequences Xₙ(M) for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for Xₙ(M) (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö’s type for Musielak-Orlicz spaces in question. This leads to a characterization of deterministic sequences Xₙ(M) (n = 0,±1,...) in terms of random measures M.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-16,
author = {Kazimierz Urbanik},
title = {Musielak-Orlicz spaces and prediction problems},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {207-219},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-16}
}
Kazimierz Urbanik. Musielak-Orlicz spaces and prediction problems. Banach Center Publications, Tome 65 (2004) pp. 207-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-16/