Outer factorization of operator valued weight functions on the torus
Studia Mathematica, Tome 110 (1994) no. 1, pp. 19-34
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
An exact criterion is derived for an operator valued weight function $W(e^{is},e^{it})$ on the torus to have a factorization $W(e^{is},e^{it}) = Φ(e^{is},e^{it})*Φ(e^{is},e^{it})$, where the operator valued Fourier coefficients of Φ vanish outside of the Helson-Lowdenslager halfplane $Λ = {(m,n) ∈ ℤ^2: m ≥ 1} ∪ {(0,n): n ≥ 0}$, and Φ is "outer" in a related sense. The criterion is expressed in terms of a regularity condition on the weighted space $L^2(W)$ of vector valued functions on the torus. A logarithmic integrability test is also provided. The factor Φ is explicitly constructed in terms of Toeplitz operators and other structures associated with W. The corresponding version of Szegö's infimum is given.
Keywords:
outer factorization, Toeplitz operator, prediction theory, Szegö's infimum, multivariate stationary process
Ray Cheng. Outer factorization of operator valued weight functions on the torus. Studia Mathematica, Tome 110 (1994) no. 1, pp. 19-34. doi: 10.4064/sm-110-1-19-34
@article{10_4064_sm_110_1_19_34,
author = {Ray Cheng},
title = {Outer factorization of operator valued weight functions on the torus},
journal = {Studia Mathematica},
pages = {19--34},
year = {1994},
volume = {110},
number = {1},
doi = {10.4064/sm-110-1-19-34},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-110-1-19-34/}
}
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