Musielak-Orlicz spaces and prediction problems

Kazimierz Urbanik. "Musielak-Orlicz spaces and prediction problems." Banach Center Publications 64.1 (2004): 207-219. <http://eudml.org/doc/286403>.

@article{KazimierzUrbanik2004,
abstract = {By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: $Xₙ(M) = ∫_\{0\}^\{1\} e^\{2πnis\}M(ds)$ (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.},
author = {Kazimierz Urbanik},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {207-219},
title = {Musielak-Orlicz spaces and prediction problems},
url = {http://eudml.org/doc/286403},
volume = {64},
year = {2004},
}

TY - JOUR
AU - Kazimierz Urbanik
TI - Musielak-Orlicz spaces and prediction problems
JO - Banach Center Publications
PY - 2004
VL - 64
IS - 1
SP - 207
EP - 219
AB - By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: $Xₙ(M) = ∫_{0}^{1} e^{2πnis}M(ds)$ (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.
LA - eng
UR - http://eudml.org/doc/286403
ER -